Daily+Summary+of+Lessons

On this page, each of you will write a daily summary of the big ideas developed in class along with any other information you want to share, such as the At Home Extension. Here is a sample format I'd like you to refer to when writing the summary:


 * ====== The following ideas were the focus of today's class: ======
 * • idea 1
 * • idea 2
 * • idea ......
 * The way we developed idea 1 (2, 3, etc) was ...
 * An important thing to remember about idea 1(2, 3, etc) is ...
 * Idea 3 (idea developed late in the class session) is something that we'll revisit in later class periods but we got a start on this idea by discussing ...

=
Please try and follow the guidelines above when writing your summaries. Avoid writing a linear "Here's what we did first, then second, and so on". The intent is that you begin to think more broadly about the ideas and find more connections; beginning to think like a teacher! So try it out. ====== I'll start the short summaries from the past few days...

1.We talked about situations where it is difficult or even impossible to find a theoretical probability. For these situations, we can use a Monte Carlo Simulation to find an experimental probability. These involve setting up a model to represent the actual question. For example, to find the probability of of a batter with a .320 average getting a hit at three out of 4 times at bat, we could draw marbles representing hits and misses, rather than actually counting the hits made by a real batter.


 * Continuing with the Monte Carlo Procedure these are the steps we followed **
 * 1. Describe a model: your model must match the key traits of your problem in order to generate random outcomes. **
 * 2. Define a single trial: understand when a single trial is complete by understanding the nature of the quantity to be associated with the outcome of a trial. **
 * 3. Conduct several trials: 100 trials are ideal, but as can be time consuming 10-30 trials will suffice majority of the time. Once the trials are complete record the quantities associated with the outcome for each trial. **
 * 4. Summarize the results: gather all the experimental data of the trials to get an estimate to the problem originally posed. **

To carry out these simulations we explored many different application and programs such as the "Prob Sim" applications and programs such as batter, shooter, and six pens. While experimenting with these programs we also learned how to manipulate them so we can get the outcome necessary. We did this either by weighting the outcomes in coin toss, or creating a seed in RandInt. Dr. B also led us step by step through a programs to explain the language and show us how to edit the programs

When working with the Shooter Program today, we also explored how to set a seed in the program by editing it and inserting it in the first line. By doing this you are limiting the outcomes so more than one person will get the exact same outcomes. This is necessary to know because this way Dr. B can give us a question on the exam and be able to monitor the correct response. Brooklyn

we also looked at the programs and need to know what to change if we want to have a diffent amount of possible incomes. Sometimes only one number needs to be changed but other times two or more might need to be edited

== We have deeply been studying the theoretical and experimental differences of probability, we need to understand the major of both and why they are different. Theoretical is without actually conducting an experiment and Experimental is when we actually conduct an experiment and we collect data. -Mallory Brownell ==

=Monday, April 11th = Idea 1: As we discussed problem #1 on page 193 these ideas came out: We decided to use both methods that were proposed to see if they both gave us the same answer or if we would get different answers. The problem dealt with using an area model and tree-diagram to analyze a two-stage experiment. In using the first model, we solved the problem as if we had a choice of one spinner or the other. Then we solved the problem using the second model where we use both spinners and we can see both outcomes. We found the probability of player A and player B winning using the second model because instead of using one spinner at a time, it allowed us to see what would happen when we spun both. We noticed that if we counted the tick marks in the square in the book on pg. 193, the ratio was the same as the ratio we calculated using numbers. Dr. B asked us to think about whether or not we could justify counting tick marks? And would it work every time?

Idea 2: After discussing the homework problem, we moved on to The Bag Game activity. Each group was given a hypothetical bag with different amounts of red and black M&M's inside and we had to determine the probability of who would win based on an area model and a tree model. Each group had different outcomes, but we decided that when we divide the box in our area model, it is based upon the probability of outcomes not the number of items in the bag. We played the game as if we replaced the M&M's each time. This differs from playing the game without replacing the M&M's. Dr. B challenged us to play the game at home without replacing the M&M's and find out what happens. This was a simulation because we simulated playing the game. Not quite yet. When we played the game on the calculator, that was the simulation. We were theoretically analyzing the game here.

Idea 3: <span style="color: #5b19a3; font-family: 'Comic Sans MS',cursive;">Continuing on we used the Prob-Sim app on our calculator. We saw that the more trials we did, the more we started to see a long term pattern in our data. In the calculator we picked marbles. We set the seed, which started the whole chain of events in the calculator. At the end of class we started a spinner activity on our calculator that we will finish at home. See question to answer below under AHE.

<span style="color: #5b19a3; font-family: 'Comic Sans MS',cursive;">Homework Problems we didn't get a chance to go over: p. 187 #4, 4c, and 5, p. 188 #5 <span style="color: #5b19a3; font-family: 'Comic Sans MS',cursive;">AHE: p. 193 #2-4, 6 Actively read p. 166 before exploration and p. 174, p. 176 #2 DO NOT do p. 169 #1-3 <span style="color: #5b19a3; font-family: 'Comic Sans MS',cursive;">For Spinner activity: How many boxes do you have to buy to get all 6? <span style="color: #5b19a3; font-family: 'Comic Sans MS',cursive;">We will be receiving our take home quiz on Wednesday. It is due Monday @ 8am. DO NOT ask any person for help. Only use non-human resources.

<span style="color: #5b19a3; font-family: 'Comic Sans MS',cursive;">good summary! -brandy

<span style="color: #000000; font-family: 'Arial Black',Gadget,sans-serif; font-size: 140%;">April 6th <span style="color: #000000; font-family: 'Arial Black',Gadget,sans-serif; font-size: 140%;">Idea 1: <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 80%;">We first discussed the differences between Theoretical and Experiment Probability and their processes. Theoretical probability is the likelihood of an outcome based on reasoning. With theoretical probability, no experiments are conducted and no data is collected, and we use ratios and decimals to represent the possibilities of an event happening. Experiment probability is the likelihood of an outcome [or an event (a collection of 1 or more outcomes)] that is computed through data collection through an experiment. An experiment is a set of trials, and trials are "one try of the investigation." To compute the probability, we came up with the equation.... __FREQUENCY OF EVENT__

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 80%;">SUM OF THE NUMBER OF TRIALS (FREQUENCY)
<span style="font-family: 'Arial Black',Gadget,sans-serif; font-size: 140%;">Idea 2: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 80%;">We then discussed the differences between 1-stage and 2-stage probability.They are used when looking at the number of events that you are investigating. They're called 1-stage and 2-stage because of the order in which you have to conduct your experiment. For example: a one-stage investigation would be the likelihood of rolling a die and getting an even number; a two-stage investigation would be the likelihood of rolling a die and getting an even number AND drawing a club card from a deck of cards. There are two models used to display multi-stage probability: using Area and using a "Tree." When using the area, we can only look at 2 stages only because we can only look at 2 dimensions. We use squares for the area because of its characteristic of 4 congruent sides; it also allows us to divide a square into fractions much easier than other polygons. The "Tree" method also allows for 2-stage probability, as well as more. In class, we only investigated 2-stage. A "tree" consists of the first stage being the "limbs" and the second stage being the "branches." Each limb and branch is a fraction of the probability that that outcome will happen, with the branches being a fraction of that variable you're looking at specifically (not to the whole, yet).

<span style="font-family: 'Arial Black',Gadget,sans-serif; font-size: 140%;">Idea 3: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 80%;">We continued using these tools for reasoning the probability of events through a worksheet that was handed out in class. The sheet had a 2-stage probability exercise in which the person had a choice of choosing between 2 hats, an the likelihood them drawing a red or white marble (There are 2 of each, so 4 marbles). The investigation had us draw the area in a grid space provided to help us visualized the probability of drawing one of the 2 colored marbles. With each problem, there was a different possibility where each of the marbles could be. **Unfortunately, I lost my worksheet and I do not have that information any longer. If anyone would like to put their investigation and what we learned in greater detail than I can without my worksheet, I would greatly appreciate it.**

__HOMEWORK:__ Read Pages 184-186. Do #3-5 on pg. 187. Actively read pages 190-192, and to #1 on pg. 193. Finish "Which is the best?" We also received the second project. It's due the last wednesday class. How about we finish up simulations on that last Wed and any time remaining will be used to examine your midterm and work on your projects. They will be due Friday, then. Would that work? If at least half of the class comes to this page and says, yes, we'll do it. It's my way of checking again if you turned on the notifications button and are taking the time to read these wonderful daily summaries everyone is writing : ) You're permitted to let your classmates know if you read this and voted. **Let's try to get everyone voting by Monday.** We also received our grade for our first project. If you believe that there may be something wrong with your grade, please talk to Dr. B about it. She'll be super helpful! **thanks**  **good summary- i will try to add the stuff once i get my worksheet from home- ashley**  **nice summary! and my vote is Yes too! -Brooklynn**

Yes- Brittany yes -Stacy YESSS :) -Paige Sounds good to me :) - Sarah Yes! -Candis -SG yes :) - Ashley yes-Mallory Anthony yup! - Brandy Pechler yes - Melissa yes - Jaelei

**April 4th**

 * Issue 1**- The first main issue that we discussed as a class today was ratios and the different ways they can be written. We started off by each determining which form(s) were correct: 1:2, ½, 1 out of 2, .5, and 50%. After reasoning through each one, we realized that all of them were mathematically correct. They are all equal to each other, just written in different ways. Two side notes that we should remember are that when adding two ratios together that are in the form of fractions, we are NOT adding fractions. So, when we have two ratios of ½ and 2/2, we add them up to get ¾ (not 3/2) because there are a total of 4 outcomes and 3 of them were chosen. The second important idea to remember is that when we are dealing with simplifying fractions, we are not doing it in the sense of making the number smaller, but instead doing it to get a fraction that is more manageable to work with. For example, if we have a fraction of 30/50, we would want to use 3/5 instead because they are equivalent to each other and working with 3/5 makes computations more convenient.


 * Issue 2-** Another main issue that came up during class was dealing with probabilities of two outcomes. We came across problems that asked for not only the probability of A and B, but also A or B. When we are dealing with probabilities that ask for two outcomes at the same time, the word “and” is used to connect them together. On the other hand, if we are looking at two outcomes in which either of them can be a possibility, the word “or” is used. We also talked about a third type of probability that is called conditional probability. This is when one condition outcome is given to us and we are to determine a probability given that condition. When we see problems like these, we should automatically think that most likely the denominator will be different than that of the probability based on all trials of the experiment. So, if we are looking at the probabilities between gender and owning a pet, and we are given that the person is a male, we now are only looking at males. If they want to know the probability of this male owning a pet, we still only focus on pet owners that are males. In this case, the category “males” acts as a subset of the population. What if the question is the probability of a person selected being a male pet-owner? Is that a conditional probability?


 * Issue 3-** These types of probabilities led us to our next main issue of CONTINGENCY probability tables. PROBABILITY tables **do not** show counts of outcomes occurring as in the contingency tables. Probability tables show outcomes and their associated probabilities. That is why we should never get a number greater than 1. I think this was your confusion this morning. We used these tables to help us see and understand the differences between the probabilities and how they can each be found find probabilities ; we would circle whichever outcome they are asking for and afterwards add up all of the outcomes that were circled. For example, if we are asked the probability of males AND pet owners, we would circle within the table all of the males who are pet owners. If we are asked the probability of males OR pet owners, we would circle all boxes that have males in them and all of the boxes that have pet owners in them. We must be careful not to get in a habit of circling the entire row/column, because a lot of the time we aren’t talking about the entire row/column but only a box within it.

Theoretical probabilities are ones that involve no testing, but instead use reasoning to make an educated guess determine the probability value. No guessing. An example of theoretical probability could be finding the probability of one outcome when tossing a common six-sided die and seeing what number appears on top. (Just want to make sure we don't think we actually will be rolling the die; rather we are __trying to find the probabilities__ associated with any outcome from such an experiment without physically using a die. ) We can use reasoning, in this case, to determine the probability values since each side has an equal chance of facing up. Our probability values for this scenario would be 1/6 for each outcome because there are 6 total possible outcomes, and each number has one chance to be facing up. Probability tables are used to help describe theoretical examples. Two important characteristics that probability tables must have are (1) each of the probability value is a non-negative number between 0 and 1, and (2) the sum of the probabilities in the table is 1. These two important factors are what we can refer to in order to determine whether or not a table is a valid probability table.
 * Issue 4-** The terms theoretical and experimental probabilities are used to describe the type of probability that we are using. Experimental probabilities involve collecting data from many trials of experiments, where the relative frequency associated with a certain outcome tends to approach and stabilize at a specific value as the number of conducted trials increases. ( The relative frequency depends on the number of trials conducted.) In simpler terms, the more trails you perform, the clearer the probability becomes. This is similar to the findings from our tossing kisses experiment. With only conducting 10 trials, we had a very different probability for landing kiss up than when we compared with 100 tosses. An example of experimental probabilities could be tossing a thumbtack and seeing how it lands (on its side or on its head) because we have no legitimate reasoning to base our probability on; we would have to conduct an experiment with many, many, many trials to provide us with a reliable estimates. Depending on the weight distribution of the thumbtack, one outcome (side or head) could be more likely than the other. However, we would have no way of knowing this unless an experiment is conducted.

Ratio- comparison of two numbers Event- collection of one or more outcomes Probability- likelihood of an event or outcome Probability table- a table that lists each possible outcome along with its probability; must contain probability values that are non-negative numbers between 0 and 1, and have 1 as the sum of the probabilities Conditional Information/Probability- when one outcome is given in an event
 * Important terms of the day:**

1) You can sit where you want for the rest of the semester :) 2) Project partners for new project- You must let Dr. Browning know if you wish to stay with your old partner, change partners, or work by yourself and why. Try to do this as soon as possible! Failure to do so will result in her assigning a partner for you. scary.
 * Reminders:**


 * AHE:** p. 159 #1-8, p. 153 #3-4, read 184-186, complete questions on p. 186

March 30th

__ 3 terms we went over were __ <span style="font-size: 16px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Variance-mean average of squared deviation <span style="font-size: 16px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Standard Deviation- is the square root of the variance/mean distance of all the data away from the mean <span style="font-size: 16px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Mean Absolute Value (MAD)- mean distance of all the data away from the mean

__**Idea 1**__- The first idea we talked about in class, was a question. I'd still say the idea was related to standard deviation. Dr B. On page 133 number 4 part A. The question was How many standard deviations are (certain numbers) away from the mean? The mean is 105 and the variance is 100. The 1st deviation to find was, 108. So we said 108-105 is 3, Since SD is squared we said 3^2 =9. So 9 is the Standard deviation. If SD is essentially a "mean distance away of ALL the data", would we find a SD of just one data value?? We found that to be wrong, because the standard deviation is 10 because you need to take the square root of the variance which is 100. V=100, SD=10. We made a number line 95-125 marked the mean, and 3 points in the problem. The mean is 105. We are looking for how many standard deviations is 108 from the mean, we found it was .3 standard deviations, because it's only 3 units away from the mean its not a full standard deviation. It is only 3/10. So the answer would be .3 SD away from the mean. __**Idea 2**__- We also reviewed ideas of mean absolute deviation as shown on page 129 and 130. 129 Shows a good example of MAD, the last column equals 3.5 which the MAD. On page 130 it shows a good example of Standard Deviation, the mean is 72, variance is 15.5 and the SD is 3.9, because you have to square root the variance (15.5) to get the SD which is 3.9. These pages are nice to compare MAD and SD. __**Idea 3**__- We went over new material //Probability// and found words that we believe are similar to the idea of probability. This was our list: Chance, most likely, ratios, probably, frequency, maybe, and likelihood. We can examine probability informally by examining a continuum that goes from never to certain. We then worked on page 141 and did A,B,C we had to individually lie a b c on the continuum below. To see what is possible and impossible, the middle would be probably. Then we continued on to #2 and placed our guess on the 1st line, then the real outcomes on the 2nd line. We did this through NAVNET. On page 144 we read about the term //random//. We can think of random outcomes as those where we are uncertain as to what will happen at a specific instance, but we know what outcomes are possible and we can predict the long-term pattern. These 3 things help when we want to use the term random. Then we did page 151 - what is the chance or probabilty of the outcomes, kiss up or kiss down(we didnt use tacks) then filled out the graphs below to see our final outcomes. So what did we notice with the experimental outcomes with the kisses?? What was the chance of having the kiss land up when you did 10 trials as compared to 50 trials? Was there a change? Then what did we find as we continued to do more trials??? The idea here was related to predicting a long-term pattern. Could we??


 * HOMEWORK **
 * -Read page 140 actively 142 #2, **
 * Read 144, Read 150 actively. **
 * Pg 152-156 #1-9 skip #2, ** #3 and #4. ** Read 157-158. **
 * Check E-mail for study groups on Monday 3-4. ** 6th Floor Commons Room Everett Tower

__**idea 1**__- The first part of class we looked at our display for Thumb Dominance and Eye Dominance. This is a categorical-categorical display. The type of graph that is appropriate to use for a cat-cat association is a stacked bar graph (also called a segmented bar graph). We found out what portion of the right thumbed people were right eyed which was found by doing (9/15x100) to get 60% This is because we had 9 right eyed people out of the 15 total right thumbed people and then we had to multiply it by 100% because that is what the total percent it was out of. We did this same strategy for the right thumbed left eyed portion and ended up getting 40% as well as doing it for the left thumbed portion which we got 64.7% for the right eyed and 35.3% for the left eyed. From here we looked at different associations such as a very strong, moderate to weak, and no association at all. We did this by placing the right eyed percent and the left eye percent into two stacked bar graphs to compare the two variables. We found that there was no association overall between both graphs for this condition (condition was defined as what we already know and it puts a restriction on what information you are looking at). The reason for this was because for both right thumbed and left thumbed they were fairly equal both around 60% and 40% so you couldn't say that if you were right thumbed then you were right eyed because for left thumb it also had about the same percent of right eyed people. In order for there to be a strong associate the middle line would have to be either closer to one end of the bar leaving one portion of it greater than the other portion. For there to be a moderate to weak association it would have to look like on of the bars where the middle bar was fairly close to the middle so you couldn't if one variable was dependent on the second variable. For there to be no association both portions or parts would have to be equal so if there were two parts then they would both equal 50%. We looked at associations where both bars were exactly the same; this would have no association because the condition is somewhat useless in the sense that both bars hold the same information so you couldn't say that right thumbed people are necessarily right eyed because left thumbed people also have a higher percent of right eyed. Another stacked bar graph that we looked at had one with right eyed and left eyed being 50% and the other one have the right eyed portion to be a lot greater than the left eyed. This would be considered a weak association because you can tell something about one graph, but you can't about the other. So overall, focusing on the middle bar in the stacked bar graph will help to identify which type of association it is, and the distance from the middle will determine the association. We also talked about using circle graphs to display the same type of information (cat-cat) because they show part to whole relationships as well. __**idea 2**__- The second main idea of class was looking at numerical and categorical data. We looked at page 48. for an example where there was a dot plot that used m and b's for each dot to represent the categorical data. We did this as a class as well by taking our pulse rates and recording it on a dot plot. Each student either places an E or a N on the dot plot where their pulse rate was located on the plot. E stood for if you exercised on average 4 times a week and N stood for no meaning you don't exercise that much each week. We looked at the plot afterwards and noticed that the lower the pulse rate the more students there were that exercised on average 4 times a week and therefore, as the pulse rate increased the more "no" occurred on the dot plot. This is considered an association because it involves two variables, however if we were looking at these two variables separately it would be considered a comparison. We also discussed while doing this activity, positive associations which means that as one variable increases so does the corresponding one creating a line. If there were no trend this would be considered "lurking variables" because there isn't an association between the two variables and other variables or things might cause this trend. __**idea 3**__- The last thing in class that we discussed was mean absolute deviation (MAD) and standard deviation (SD). We looked at a balance scale that had 70 as the balance point or the mean. To find the mean deviation we would have to add all of the deviations (distances are only positive; deviations consider if you are above or below the mean) away from the mean and divide by the number of total data values, n. This finds how far away the deviations are from the mean, which is always zero because of the definition of a mean. However, you need to apply the absolute value to get rid of the negatives on the deviations; this produces distances. So the absolute mean deviation is defined as the mean distance of all the data from the mean average. The standard deviation does the same thing, finding the distance from the mean average, however instead of finding the absolute value you just square the deviations to get rid of the negatives. We looked at two box and whisker plots with the same min and max to help us visualize MAD and SD. We found that if a box and whisker plots min, Q1, med, Q3, and max were further spread out then if they were all fairly close that the standard deviation would be larger, but not by much because the minimum and maximum values still are the same. Therefore, we said that MAD and SD are both measures of variability or spread of the data.
 * March 28- **

**Homework:** eye dominance stacked bar graph pg 69, read pgs. 66-68, complete pg 69: 1, 2, 3, read pgs. 128-131 and complete pg. 132: 2, 3, 4.

<span style="color: #006cff; font-family: 'Arial Black',Gadget,sans-serif;">﻿Also, we talked about how to look for trends on the dot plot for num-cat associations. In our pulse data, most of the n's were higher on the number line. This would be considered a trend or association. <span style="color: #006cff; font-family: 'Arial Black',Gadget,sans-serif;">Good summary! -Candis =** March 23- **= **Idea 1-** The question we looked at was why it was inappropriate to use a double bar graph to compare arm span and height. We stated that you couldn't see the overall patterns and relationship along with not being able to make predicitions off of one variables based on the other. We also were reminded that bar graphs are great for categorical data but not for comparing 2 numerical values. We discussed how looking at scatter plots allows us to see the overall relationship between the 2 variables along with being able to look at one variable and predict what the other number would be. **Idea 2-** We discussed how to find the linear regression line (the mathematical line of best fit) and what it does. We determined that it almost acts like the mean where it is a balance point. The regression line allows us to try to get as close to everything balancing out from one side of the line to the other. It takes the vertical distance (Deviation) between the points to the line and tries to make the left side of the line and the right side of the line be as close to zero as possible. We also stated that the line of best fit(The line that we draw) is only accurate for our data points given not to be able to try to predict others. I'm not exactly sure of your point here. Are you saying that when we MANUALLY find a line of best fit, that the line we find will probably not be the same line that another person finds? If so, that is true. But, when I do find my line, I CAN predict other data values from that line. I'm not sure what you meant about the prediction statement. Dr B. If the line of best fit is drawn correctly it should be going straight through the origin (the point 0,0) or as close to it as possible. Not exactly. When the context of the problem indicates that the origin makes sense, they we should TRY to get our line as to pass through the origin or as close as we can. Technically speaking, our height and armspan graph could have passed through (0,0); if you have no height then you have no arm span. HOWEVER, we only collected data from adults and not children so our line couldn't be forced through the origin; it just didn't work. So, we only try to get our line to go through the origin when it makes sense to do so. We do NOT have to do it always. Dr B. When we drew our best fit line the class in general had the b part of the equation y=mx+b equaling something that was an astronomical number (-50 to -80) This is not appropriate for this data set due to this meaning that when a baby is born and is only 21 inches their arm span could still be negative or so small that it would not be proportional

Homework- p 67, use the data from p 31 (eye and thumb) and add it into the cells we created during class on p67 and also page 69 #1 Survey project is due on Wednesday

I like how you are all trying to discuss ideas now instead of just describing how we worked through problems. Good job. Dr B = In Class Lesson- March 21, 2011 = The next part of our **survey project will be due next week Wednesday March 30th**. At least for now.

The following ideas were the focus of todays class: **Idea 1**: On page 21 there is a box and whisker plot that we went into depth about the upper and lower quartiles and how many numbers are in each considering that we had a total of 35 sets of data. Each part of the box and whisker plot is to be referred to as a fourth and we found out how many parts of our data were in each fourth. Through discussion we figured out that you could take the total number of data points subtract 3 and then divide that number by three 3 or 4?? and that will give you how many numbers are in each fourth. This works because the number for the LQ median, Median, and UQ median are all separate numbers from the data in each fourth. This equation is not something we need to use but it really helped some students understand how the data is distributed in a box and whisker plot. **Idea 2:** "Outlier" is 1.5 boxes away from quartiles. We were figuring this out by measuring with our hands at first and then we decided to found a mathematical procedure to actually figure out if a number was an extreme or an outlier. We used problem #2 on page 122 to help us further our understanding of this. For Textbook B the box length is 30. If we need 1.5 of the box length we would take the 30 Box length, divide by 2 (15) and add that to the original to get 45 box length of 1.5 box. We could also just multiply 30 by 1.5 to get 45. We wanted to see if the whisker at 20 was a n outlier and it was very hard to tell just by looking at it, so we took the length of 45 and found that in order for there to be a outlier it needed to be at 15 and 20 was not considered a outlier. Although 20 was considered an extreme because it's the min and far away from the data. A outlier will always be an extreme but an extreme will not always be an outlier. **Idea 3**: We used our calculators to get all of our class data for height and armspan. We wanted to see if there was a relationship or association between these two variables. We found that the best way to see if there was a relationship would be to make a scatter plot. Height is the independent variable(X.) Arm Span is the dependent variable(Y.) We placed the information into our calculator and made a scatter plot using this method. The data on the scatter plot displayed a trend or pattern in their clustering. We could see this trend as the points were clustered somewhat along a "trend line" that started in the lower left hand portion of the graph and moved upwards towards the right hand side of the graph. We noticed that as the height of a student increased, so did their arm span. We used the manual fit option on the calculator to manually fit a line to the data. We then found that there are different associations that the data on a scatter plot can have with each other. **Strong negative association with trend line**-The data has a strong trend and visible line where there is obviously a strong relationship between the two variables. **Moderate positive association with trend line**-The data does have some association but it varies so it does not have a strong line. **Weak to no association**-No trend in the scatter plot is observed, the data seems to be scattered in a random way.

//__ Homework: Read and complete exploration of pages 72-74, complete #2 a-d, 4(label the data county, cig, and mort and put into 3 lists) 6,8 __//

-LOOKS GOOD! -QUIZ WED THE 23RD! -Sarahhh

<span style="color: #811bde; font-family: Verdana,Geneva,sans-serif;">﻿Lesson 15- March 16th
====<span style="color: #811bde; font-family: Verdana,Geneva,sans-serif;">Idea 1: Starting off the morning we talked about plotting histograms and box plot (box and whisker plot). The minimum point represented on both diagrams should have the exact same value but the maximum of the histogram and the box plot will not have the same value. The maximum line on the box plot goes up to the beginning of the interval including the whole number but does not include the following number. We also discussed that frequency of a table represents that you can only count the data once, or depending on how much you change the frequency too. If you change the frequency to three, it will count that data set three times. ==== ====<span style="color: #811bde; font-family: Verdana,Geneva,sans-serif;">Idea 2: We talked about the main ideas considering a box plot. A box plot can show some spread and variability of the data but is limited when it comes to the distribution. A box plot is created to show the difference in medians based upon the whole data set, the upper quartile, the lower quartile, and also displays the lower and upper extremes if had any. ==== ====<span style="color: #811bde; font-family: Verdana,Geneva,sans-serif;">Idea 3: Lastly we plugged into our calculators, a lot! First, we all made data sets with the same means <span style="color: #000000; font-family: Verdana,Geneva,sans-serif;">(did they all have the same means???) <span style="color: #811bde; font-family: Verdana,Geneva,sans-serif;">and amount of numbers in the data but each had different values. We proved that even though each data set was different, the box plot ==== ====<span style="color: #000000; font-family: Verdana,Geneva,sans-serif;">were identical but the <span style="color: #811bde; font-family: Verdana,Geneva,sans-serif;">histograms <span style="color: #000000; font-family: Verdana,Geneva,sans-serif;">looked very different. So data sets with the same 5 critical values for box plots can have very different looking distributions of data <span style="color: #811bde; font-family: Verdana,Geneva,sans-serif;">. ==== ====<span style="color: #000000; font-family: Verdana,Geneva,sans-serif;">Idea 4: <span style="color: #811bde; font-family: Verdana,Geneva,sans-serif;">Next, we wanted to find the mean of the mean. <span style="color: #000000; font-family: Verdana,Geneva,sans-serif;"> Not quite; the **mean of the distances of the data values from the mean.** We were looking for another way to describe the variability within a data set other than using a box plot. The question was "can we describe variability with a single number?" I think this section needs some reworking. There are correct pieces but they are mixed with other ideas that so one can be misled. <span style="color: #811bde; font-family: Verdana,Geneva,sans-serif;">Making another list calling it L4 we wanted to balance out the distribution and see what was the mean of our data set away from the balance point. "The value of x can show the distance of a number away from the mean." When the outcome had a negative number, that shows how much greater the jump is away from balance point. That is why we took the absolute value of the whole set to make each number a positive number. The reasoning for this was to get the total distance away from the mean. We took the mean of the mean because with both positive and negative numbers in the set, the column total added up to zero. When zero is the total, it gives us no idea on how "zero numbers" can be distributed. The absolute made everything positive to show the cluster of the data in that distance. ====

<span style="color: #811bde; font-family: Verdana,Geneva,sans-serif;">Work: Read pages 127-131 and do explorations 1-3

 * <span style="color: #006cff; font-family: Verdana,Geneva,sans-serif;">Good Summary! But just as a reminder the survey project due date got changed to Monday in class! -Brooklynn **

<span style="color: #0095ff; font-family: Georgia,serif; font-size: 120%;">__Idea 1:__ The first main idea that we talked about in class today was the range of a data set. It can be explained by saying it is the variability or spread of the data. The range can be found by finding the difference of the min and max value of the data set. The higher the difference, the larger the range is. To help us understand it better, we looked at two different data sets and compared the ranges of each.
 * <span style="color: #0095ff; font-family: Georgia,serif; font-size: 120%;">Lesson 14- March 14th **

<span style="color: #0095ff; font-family: Georgia,serif; font-size: 120%;">__Idea 2__: The next main idea that we focused on was quartiles. To find the upper and lower quartile of a data set, you first split the data in half at the median, or middle value in the data set. Next, you find the median/middle number of each half, without including the median of the entire data set. The value that you found on the upper half is called the upper quartile, and the value on the lower half is called the lower quartile. Example: <span style="color: #0095ff; font-family: Georgia,serif; font-size: 120%;">1, 2, 5, 7, 9, 12, 15 – In this data set, 7 would be the median of the entire data set. The lower half would be 1, 2 and 5, with 2 as the lower quartile since it is the middle number within the 3 numbers. The upper half of the data would be 9, 12, and 15 with 12 as your upper quartile because it is the median of the 3 numbers. <span style="color: #0095ff; font-family: Georgia,serif; font-size: 120%;">The quartiles are based upon the position of the number within the data set rather than its actual value/distances from the other data points.

<span style="color: #0095ff; font-family: Georgia,serif; font-size: 120%;">__Idea 3__: The last main idea that we talked about was box and whisker plots. We worked on page 120, which is where you can find an example of this type of plot. On the plot, we found and labeled the min and max, lower and upper quartile, median, and lower and upper quarter. The min and max were the highest and lower points on the plots. The lower and upper quartile were the verticle lines on each of the end of the box, where the box ends and the whiskers start. The median is the line that splits the box into 2. The lower and upper quarter are the horizontal lines that extend out from the box, known as whiskers. After working with this example and going through the questions below it, we then created identical box and whisker plots on our calculators.

<span style="color: #0095ff; font-family: Georgia,serif; font-size: 120%;">Good summary! Brandy

<span style="color: #ff0000; font-family: Georgia,serif; font-size: 120%;">What may be good to include here are some of the misconceptions that may arise as people try to interpret the box and whisker plot (or box plot). Perhaps Idea 4 could relate to that?


 * <span style="color: #0095ff; font-family: Georgia,serif; font-size: 120%;">We also changed seats into new groups, as well as received our grades on the Midterm. **


 * <span style="color: #0095ff; font-family: Georgia,serif; font-size: 120%;">AHE: read pg. 117. Complete pg. 121 # 1, 2, 4a, c (need data from 3b), 5, 7, and 8. *Part II of the survey projects are due Friday. **

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Idea 1: We looked at Page 99 #1. We discussed that once you know what the mean is you can show it by a different chart. Instead of having your data all spread out on the number line you could show it with all of the markers at the mean. We discussed that this would be considered a leveling off method. We compared this with having 5 or 6 small buildings and 1 large one. We would take from the large building (or block set) and share with the others. ======

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Idea 2: On page 106 #2. We discussed that Davey's method in a formula would be X (x being the number you are looking at now) plus 1 and then divided by 2 will give you the median number. Ex: If the number is 15, the median number would be 15+1=16/2 which would be 8. This means that the median number of a 15 number set would be the 8th position. ======

We did not get a chance to finish discussing the other problems that we had questions on, so those will be discussed on wednesday. We have an exam on Wed so no further discussion.
I thought we discussed more than just two ideas?? Didn't we also talk about using a balance approach to a problem and then contrasted that to an algebraic approach?

-during part 2 we do not need to have the measures of spread (vulnerability)

 * Good Summary! Brooklynn **

<span style="color: #ea2a65; font-family: 'Comic Sans MS',cursive; font-size: 120%;">**Idea 1**: We looked at page 61 in the book. In our groups we compared our frequency tables and decided that since the problems says the numbers were already rounded that we could leave off the hundardths place value or have the place value of 4 in the houndardths place. Because the number then would round up into the next interval. The points on the number line are the begining points of each interval and worked on the end points and how to tell. <span style="color: #ea2a65; font-family: 'Comic Sans MS',cursive; font-size: 120%;">**Idea 2**: Still on page 61 looked at letters f and g. We made up the data and put it in the double stem bar graph then had it all intered into to the caculators useing the activity center on navinet. Then we constructed a histogram that looked like the one in our book. Which <span style="color: #ea2a65; font-family: 'Comic Sans MS',cursive; font-size: 120%;">entailed, going to the window display and changing the settings. If wanted to just use the graph on the calculator, then can use the trace button to do so. Then arrow back and forth to see the actual values. <span style="color: #ea2a65; font-family: 'Comic Sans MS',cursive; font-size: 120%;">**Idea 4**: Again we reviewed the difference between numerical and categorical data looking at number 3 on page 105. If we were graphing the sales then it would be numerical but since it asked what the customers perfered then it categorical data. Then we briefly discussed what kind of graph would be approiate to represent this categorical data. The context of the problem helps use figure out what to use.
 * <span style="color: #00a8ff; font-family: 'Comic Sans MS',cursive; font-size: 120%;">Lesson 12﻿ ﻿Feburary 23rd **
 * <span style="color: #ea2a65; font-family: 'Comic Sans MS',cursive; font-size: 120%;">Idea 3: **<span style="color: #ea2a65; font-family: 'Comic Sans MS',cursive; font-size: 120%;">Next we looked at the measures of centers. It was clarified that bumps in data can be considered the mode. But you can't use bump in intervals because we don't know the raw data and what occurs the most often. And Range is the actual difference beteen the max and min. Then looking at all 3 kinds of measure of centers we compared how similar they are to each other in a skewed graph of the one on page 61. We discussed a little about why those numbers may be a little off from each other.

<span style="color: #ea2a65; font-family: 'Comic Sans MS',cursive; font-size: 120%;">Surveys due @ 10 put on goggle docs <span style="color: #ea2a65; font-family: 'Comic Sans MS',cursive; font-size: 120%;">writing assigment writing assignment due the friday after we return from spring break, just emailing it is fine (if you complete it before the due date feel free to submit it anytime) - Brandy
 * <span style="color: #ea2a65; font-family: 'Comic Sans MS',cursive; font-size: 120%;">Homework: **<span style="color: #ea2a65; font-family: 'Comic Sans MS',cursive; font-size: 120%;">Finish AHE from Monday with pg 116 #19 in additional.

<span style="color: #006cff; font-family: 'Comic Sans MS',cursive; font-size: 140%;">Lesson 11: February 21st

**Idea 1**: We talked about measures of center; Mean, Median, and Mode, again today. Each group came up with something that we could say about the mean, median, and mode that a child would understand. For example, for mean we came up with; make all equal, redistribute, and balance point. For Median, we said middle. And for mode we said most common. Then we looked at number 3B on page 98 and found the missing value, which was 90. We determined that you can think of the mean as a fulcrum. **AHE**: <span style="color: #006cff; font-family: 'Comic Sans MS',cursive;">Pg. 99 #1-3,5-9 <span style="color: #006cff; font-family: 'Comic Sans MS',cursive;">Read Pg 102 and through the explorations to clarify ideas developed in class today <span style="color: #006cff; font-family: 'Comic Sans MS',cursive;">Pg 104 #2 <span style="color: #006cff; font-family: 'Comic Sans MS',cursive;">Pg 106 #2-5, 7-12, 13A, 14-15 <span style="color: #006cff; font-family: 'Comic Sans MS',cursive;">This Homework is set across Monday and Wednesday this week
 * Idea 2: ** A problem we completed is described here; what would one say is the "idea"? We then looked at Problem number 2 on page 97. We talked about why the mean was 13, without actually doing the "add all the numbers up and divide by the number of numbers" math. We found the distance from the tops of all the bars to the mean line. We found that the sum of the distance for the bars above the line was 11 as well as below the line. Since the two distances equaled we knew that the mean was right. Be prepared to explain why if the distances are equal, that meant we had found the mean.
 * Idea 3: ** We did 2B on page 98. This problem was a little more difficult. We determined that the distance from the bars above the line was 60 and the distance from the bars below the line to the line is 35. Since the values were different we knew that the mean line of 65 was not right. However, we needed to find a method to find the correct mean without guessing and checking. We decided that we would take the difference between the top and bottom (60-35=25). Can you describe what the number 25 represents in the problem? Then we divided 25 by 5 (the number of bars in the problem) and we got 5. We moved the mean line up 5 then from 65 to 70 and then we found the distance between the tops of the bars and the mean line. The values were 50 on top and 50 on bottom, so we knew that our mean was right. Again, how do we know the mean is right when this happens?
 * Idea 4: ** We used a balance point (like a balance beam/teeter toter) to find the mean for #3 on pg 98. We wanted to have 4 numbers that had a mean of 50. We knew that the 4 numbers had to add up to 200 (4x50=200) I didn't know you used that information; remember, your students won't. I was hoping you would just try to visualize what balanced data might look like and go from there. so one set of numbers we came up with were; 60,40,70,30. We put 30,40 on one side of the fulcrum (the fulcrum value was 50) and 60,70 on the other side. It balanced because the distance from each of the numbers to the fulcrum was the same on both sides. For example; 50-30=20 50-40=10, so 30 on one side. 60-50=10 70-50=20, so 30 on the other side.
 * Idea 5: ** We did Pg 103, number 1. We found the median incomes for both schools. We got $31,500 for Keats and $36,250 for Longfellow. The median for Keats was easy to find because it was an actual salary. For Longfellow we came up with 2 ways to find it. You could either take the two values that the median falls between and add them together and divide by two (35,500+37000/2=36,250) or take the difference between the two and divide that in half and add it too the lesser number (37000-35500= 1500 1500/2=750, then 750+35500=36250)

We will get our quiz back on Wednesday <span style="color: #006cff; font-family: 'Comic Sans MS',cursive;">Also we will be changing groups after spring break.

<span style="color: #00a8ff; font-family: 'Arial Black',Gadget,sans-serif;">﻿We talked about the difference between the median and mode <span style="color: #ff0000; font-family: 'Arial Black',Gadget,sans-serif;">(I think you mean "median and mean" here vs mode) <span style="color: #00a8ff; font-family: 'Arial Black',Gadget,sans-serif;">too, and how one of them might describe the data better under certain circumstances. Like when we compared the two schools (Idea 5) the median actually described the data set better because of the extremes involved in one of the sets. <span style="color: #00a8ff; font-family: 'Arial Black',Gadget,sans-serif;">Good summary! - Candis <span style="color: #5b19a3; font-family: 'Arial Black',Gadget,sans-serif;">Good Summary, I think you covered everything! Brooklynn

Lesson 10: February 16

First in class we looked at the raw data collected by our pilot surveys and discussed our accuracy of randomness achieved. Our variety of majors was very diverse which was pleasing, but a majority of majors were education which is to be expected considering the college of education is big here at Western.

Next we discussed what we have learned so far about the survey process. So far we've posted the research question, collected the data and started to analyze the data. We have gone over the process of analyzing the data by looking at single variables, looking at bumps, clumps and gaps, min-max range, overall shape of a graph constructed through data, and if the shape is symmetrical or skewed. We have also worked with organizing data and comparing it through stem and leaf tables. We also talked about how analyzing and organizing are part of the same piece. You have to organize in order to analyze.

Finally we discusses a new idea, measure of center. To start off we learned visually through unifix cubes and looked at a table of student family numbers and discussed how the 4th graders would brainstorm to determine the average/typical number of people in these 7 house holds. The ideas that the class came up with were 1. 4th graders would just assume the highest and most frequent number would be the average and most typical. Especially with the physical display of the data towers in front of them. 2. They would take apart all the cubes and distribute between 7 groups to gather an average of 4 per household. Also known as the mean. We then went into the idea that our knowledge of average is biased to the mean because we are so used to taking a whole and dividing it by the number of groups and then finding the average, when in reality the average refers to all mean, median and mode, it just depends in what context you use each.

AHE: 5 more people surveyed by Wednesday (2/23) at 5pm Actively read p. 96; complete p. 97 #2 and p.99 #1 and 2 Actively read p. 102; complete #1 in Exploration

**Lesson 9: February 14**


 * Idea 1: **﻿﻿This morning we spent much of our time negotiating which data displays are most appropriate for categorical and numerical data. The class came to the conclusion that numerical data is best displayed using dot plots, histograms, and stem and leaf plots. When analyzing numerical data, these display types are most convenient because one can simply look at the display to determine the minimum, the maximum, and the range of the data set. Categorical data is best displayed using bar graphs, circle graphs and picture graphs. These display make it easy to determine the frequency each category.


 * Idea 2: **We also reiterated the differences between a bar graph and the histogram; the main point being that the bar graph has spaces, where the histogram does not. Also, a bar graph may have ranges, a histogram has values on a number line (this can be seen on pg. 56). A consistent scale is important in a histogram, when using a bar graph a scale is not important.


 * Idea 3: ﻿**The class period was also spent navigating stem and leaf plots. Using pg 52d of our homework as a model we determined step and leaf plots to be place value charts, used to easily find the min, max, and range of a data set. Clumps, bumps, and holes were also reviewed. Clumps being a cluster in the display, bumps being the highest interval, and holes obviously being a section in a number line were no data is presented. Observable patterns in the data were also looked at. Skewed data illustrates a set that has outliers, were the data may slope off (if data is sloped on the right is is said to be skewed right pg. 61). Symmetric data is shows a visible fold line, where each of the side of the graph is symmetric.


 * Reminders: ﻿**
 * Quiz will be Wednesday** over information presented to us thus far

AHE: pg 87 #1,3,5,6

Survey project: Dr. B handed out the raw data from our pilot survey, we have decided to not make any changes to the questions. Part one of out survey project will be due Friday by noon!!! Handed in with part one must be the four survey questions you and your partner completed... If you are unable to turn in part one Wednesday in class you may bring it to the math department (3rd floor of Everret tower) Friday by noon. You may also email it, but again don't forget to turn in your survey questions!

** Lesson 8: February 9 **

 * Idea 1: ** At the beginning of class finished discussing our pilot survey questions and finalized which questions we're going to ask and in the form they are to be asked. Each of us has to survey two people for our pilot and they are due by Saturday night at midnight and are to be reported to google docs. Dr. B emailed each of us the final form of the survey questions.


 * Idea 2: ** The main idea we discussed today was representing data appropriately. When displaying data, the range should be easily identifiable, along with the minimum and maximum values and any gaps or breaks in the data. The two main graphs we compared were histograms and bar graphs. A histogram is best used to display numerical data, with continuous intervals and no gaps between the bars of data. Bar graphs have gaps between the bars of data and are best used to represent categorical data. For examples, we compared the histogram on page 62 and the bar graph on page 63. When looking at the histogram, it is apparent that intervals on the bottom of the graph are continuous and the gaps between the bars represent a gap/break in the data. If you look at the bar graph on page 63, you can see that there are gaps between the bars of data, but that does not mean that there is a gap in the data.


 * Idea 3: ** The last two displays we touched on were picture graphs and dot plots. Dot plots should be reserved for numerical data and picture graphs require picture icons that symbolizes the data.

Complete pilot survey and enter data on google docs by Saturday at midnight. How did you get representative sample? (Part 1 of Survey Project due 2/16) Mystery Balancers Worksheets: Dot Plots Histograms: pgs. 58-65 #2-4
 * Homework: **

Good Summary - Melissa I think you covered it all! Good job! -Ashley Don't forget to think about which display is the most appropriate for the data that you are representing. I have a feeling this will be important for the survey project. Good summary! -Candis


 * Lesson 7: February 7 **

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Idea 1 : ﻿This morning we spent time on previous homework problems involving the stacked bar graph on page 37 # 5A figuring out what the "Do you believe in aliens?" variable was. Agreeing that this specific displayed was a categorical graph. We also discussed the "Tobacco Industry Contribution" on page 36 # 2C. We tried to determine what variable this was either numerical or categorical. We agreed that this graph was categorical and not to get confuse that as a numerical just because the graph displays numbers. The category in this graph is the Democratic and Republic Party. We will be going back to discuss # 2C until we all agree with the same answer. We are still trying to agree on if Admed's statement "Democrats receiving more donations from the tobacco in 1995-96" is true or false. ======

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Idea 2: ﻿Another important lesson we talked about was the class date pulse rate graphs and created the circle graph for out M&M data. The pulse rate data was from our PIQ and we had to make a graph displaying all of the information. Our M&M circle graphs were formed from making our original stacked M&M graphs and taping the ends together in order to make it a 3D﻿circle and draw it out on a blank circle. We also had to find the percent of each color (such as, there were 14 blue M&M out of the total 55. Take 14/55=...) and the angle measure with using the angle tool to calculate that. That was also shown on a calculator by taking the answer to the 14/55 and multiplying that by 360*. (14/55= .2545454545. then .2545454545x360* is a angle measure of 91.63636362). ======

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Idea 3: ﻿Lastly we talked about keys to numerical data. You may order numerical data in various ways such as a stem & leaf plot, dot plot, histogram, etc. They can all show the high and low numbers, the mean, median, and more but the organization can be presented in many different ways. ======

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<span style="color: #6b16c0; font-family: 'Times New Roman','serif'; font-size: 12pt;">Homework: <span style="color: #0d0b0e; font-family: 'Times New Roman','serif'; font-size: 12pt;">﻿Read pages 41-45 actively. Use the PIQ on Google doc. of our arm span and height and do pg. 47 #2. ======

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<span style="color: #0d0b0e; font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: normal; margin: 0in 0in 10pt;">Pg. 48 # 1-2 (use page 31 to help with #2) # 5A, 6, 8, and 9. (Only refer to the first student explanation for 6A). ======

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<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">- <span style="color: #0d0b0e; font-family: 'Times New Roman','serif'; font-size: 12pt;">Remind: The Survey Projects first project is no longer Due on Wednesday. Also, make sure you make an appointment soon. The last day to do this is February 18th and that must scheduled before February 11th. Good reminder! Dr B =====

Good summary!! We are also keeping track of our points this semester. Find somewhere (in your book, planner, or anywhere you won't lose it) and record the scores you get from writing assignments, quizzes, etc.) -Mallory A.

Good summary I think you summarized everything very well and thanks for the reminder about the appointment. -Mallory B

<span style="color: #ea2a65; font-family: Georgia,serif;">^^Great! Good details and examples. I am drawing a blank and cannot remember what making an appointment is referring to, could someone help to specify this more so I understand? :( thanks! -Paige R

Yeah, look in the syllabus on the white sheet of paper that is stapled to the bright yellow sheet. It's under "Class Participation Rubric" at the bottom of the first box. It's the bold print that says we have to make an appointment with her just to sit down and discuss homework and whatever else you need to talk about. - Jaelei

<span style="color: #1758ba; font-family: 'Arial Black',Gadget,sans-serif;">﻿Lesson 6: January 31
-Create a display of our class pulse data. This was given to us in class, but the numbers are 54,72,74,70, and 73. Oops! I really want you to use ALL of the class data, not just the 5 I randomly picked. That was just to show you an example of how technology may do things that because you can make it do something but what you had it do, makes no sense! The calculator doesn't think for you. Sorry about that confusion. USE ALL PULSE DATA. -If you haven't already, look over your commented paper, give yourself a grade, and bring it back to Dr. B on Wednesday. We aren't rewriting, just grading based on her comments! Also, feel free to ask me any questions on the comments. My hope is that your careful reading of the comments helps you to understand the task and key ideas better as well as understand the final grade.
 * Idea 1:** We spent a lot of time today talking about the homework problem from Wednesday. We finally came to the conclusion that the percent __increase__ in the number of prisoners from #8 had to be found by finding the difference in prisoners from 1980 to 1998 (3159-295) and then dividing that difference by the number of prisoners we started with (295). Using this equation we found that the actual increase was 970.85%. (Emma posted another good explanation on "I have a question on..." if you want to go over it again). The problem made more sense to many of us after we split the problem into several parts (find the difference in prisoners, THEN figure out what the starting value was, THEN find the percent of increase). Also, comparing a problem about increase/decrease to sale prices can be very helpful. For example- a dress is regular price $100 but is on sale for $76. What percent is discounted? To find out, subtract the new price from the starting price, and divide that amount by the starting price.
 * Idea 2:** Another important point from today's lesson has to do with the use of our calculators. To create a new list, hit LIST, go to a blank list, go up to the top, and create a name using the text function. Don't forget that to make items in your list categorical entries, you have to use quotation marks around just the first entry. To create a graph from data in your lists, hit 2nd PLOT which takes you to the plot page. From there you can turn the plots on or off, choose which type of graph suits your data best, and enter which lists the graph should take data from.
 * Idea 3:** While I'm on the subject of displays... make sure to determine what is appropriate to show your data! Bar graphs, pictographs, and circle graphs are for categorical data! *hint* the homework uses numerical data, so don't use any of these types of display! It is also important to remember that frequency is not data! The frequency tells you something about the data, but remember that the number of times an answer occurs is something completely different from the data.
 * <span style="color: #1758ba; font-family: 'Arial Black',Gadget,sans-serif;">﻿Homework! **
 * -**Using the display from #4 on page 37 (Oatmeal Toppings) create a read question, a derive question, and an interpret question. To clarify what these types of questions are, see pages 32 and 33.

Good Summary Candis - Melissa I think you covered it all! Ashley

LESSON 5 January 26th This exercise truly shows us to challenge statistics presented to us.
 * Idea 1:** One main idea we focused on was the importance of rounding decimals when representing a statistic in percent form. It's important to do that when representing a set of data because, depending on which way we round, we may add or subtract another "percent" in a certain area of data, which can result in the losing or gaining of accounted or unaccounted data. On page 37, #4 is an example of a set of data that's percents don't add up to 100 percent, as a result of rounding the values . We decided as a class that rounding to the nearest hundredth place was the best.
 * Idea 2:** Another important idea we discussed was the idea of how to find a percent in data whose data range doesn't start at 0. The example that we look at was on page 11, #4, in our text. To solve this problem, we need to understand that we cannot simply believe that statistics that are given to us are true, so we need to be able to test their math. For this example, steel output was at 4.2 million tons of steel per year in 1928, and Stalin's plan was to have steel production increase to 10.3 million tons per year by 1933. However, by 1933, the steel production had increased to only 5.9 million tons per year. According to the Kremlins, 57 percent of their plan had been fulfilled. However this is not the case because the data range starts at 4.2 and not 0. To find the percent of change in this data set, you need to start by finding how large your data set is by subtracting the maximum of your range by the minimum; in this case our range is 6.1 million tons (10.3 - 4.2 = 6.1). Because you started at 4.2, you now need to subtract 4.2 from 5.9 because that difference is the amount of change from the minimum of our range to where we are now. So, our increase is 1.7 million tons. Now, because 1.7 is a fraction of 6.1, we need the ration of 1.7/6.1 to find what percent of the plan has actually been fulfilled. So....1.7/6.1 = .27868852, now multiply by 100 to get the percent, which is (with appropriate rounding) is approximately 27.87 percent.
 * HOMEWORK:** Finish Pg 11 #4. Actively read pg. 32-33. Pg 40, # 8. Find the percent of decrease of each set of data, with 1980's population being 500, and 1998's set having 6,542.

Also Remember there is a quiz on Monday.-Allison

Remember as well that when comparing data be sure the data is relative, meaning you are comparing two of the same "wholes"... Dr. B used the example of candy bars: 50% of a fun size snickers is not going to be the same as 50% of a king size candy bar. We discuss this concept using problem #8 (page 40) we could not compare prisoners from 1980 to those in 1998 because we have no way of knowing that the sets of data are the same, it is likely the values have fluctuated throughout the years.

Dr. B also gave us a tip: if you are having trouble with a problem it may be helpful to draw a picture of work the problem backward

Lesson 4 January 24th -The following mathematical ideas were the focus of today's class We also went over categorical and numerical answers. //Categorical// is a respnose with some type of grouping related back to the question. EX. what's your favorite color?-PINK //Numerical// is a response using a count response or measurement. EX. How tall are you?-5'4'' -Full-time student -**ON** Main Campus -Undergraduate -Students who have a job -Wmu Student(Male&Female) We talked about the problem on page 10 #2 in our book. We voted which answer would be the best A B C D? The most popular vote was B. Then we discussed all of the answers to find out why they weren't the best. Answer A was systematic sampling, which means you already have a system planned and ready to use. B was random sampling, there is no bias. C. Was Convenience sampling b/c it was just in Mrs. Lo's class and convenient. D was volunteer sample, they would have to volunteer to bring it back. HOMEWORK!! -Send an e-mail with at least two survey questions by MIDNIGHT, that relate to our main question. -Then after Mrs. B reviews and e-mails you back with the most popular, you will send her your TOP 8 questions by TUES. MIDNIGHT! -Pg. 35-40 #2, 4-6, 8
 * Idea 1:** We talked about the process of statistical investigation, and defined analysis and interpretation. We said that //analysis// is organizing the data and graphing/displaying the data. Interpretation is making conclusions and translating data (making it understandable.)
 * Idea 2:** We focused a lot on our survey question, which is "How does working at a job affect a full-time undergraduate WMU student?" We had some problems on how specific we wanted the question to be so we logged into our NavNet on our calculators and made a vote. One problem we found was if we survey someone and they don't have a job should we still include them? which turns the question into "Does working at a job affect a full-time undergraduate WMU student?" We voted and majority ruled. The 1st question. Other issues we ran into were was what kind of working, volunteer workstudy, stay at home mom etc. We decided that we can use them in our survey questions.
 * Idea 3:** What's our population for our question?
 * Idea 4:** Sampling

-Sarah Lundgren

Very clear and detailed explanation. Thanks for posting the difference between analysis and interpretation of data! -Brittany N.

-The following mathematical ideas were the focus of today's class:
 * Lesson 3 January 19 **
 * Idea 1: ﻿** We focused on the process of statistical Investigation. The process of statistical investigation is referred to on page 1 of our handbook. They are the actions on a data set including collection, organization, summarization, and interpretation. This led us to the discussion of where we are right now in the process. We came up with the list of what we have done and where we are right now in the process: (asking questions, collecting the data, and organizing the data).
 * Idea 2: ** Our class voted on a research question that wanted to do which ended up being, "How many students in our class go to classes and have a job?" From this question, we were thinking of ways to revise it to make it more clear. We came up with using WMU students on main campus as our population instead of just those in our class to make our population larger and to less bias. If we were to just use those in our class we are not including males in our population which could be looked at as being bias. We are still coming up with ways to revise this research question which is part of our AHE. We are suppose to post our questions on the wikispace by Saturday night. We also discussed sample and target population. Our target population is who we are going to be surveying for example: WMU main campus students. Each of us need to come up with a target population for this research question for class on Monday.
 * Idea 3: ** As a class we looked deeper into the organizing step of the process. The M&M activity helped us to understand different ways to organize data depending on which grade level you are dealing with. Prior to, we developed the question: "What is the distribution of the colors?" Relatively speaking, "How many do they make of each color?" Each group was given a certain grade level and from there we came up with different graphs and displays. K-1 used a picture graph by sorting the six different colors. This is known as real display because it is dealing with the actual M&Ms because we left them there. We discussed the difference between categorical vs. numerical. Categorical- frequency isn't the data and Numerical- is it measurement or count? Grades 2-3 dealt with using picture graphs to develop a bar graph. Picture graphs deal with icons verse the actual M&Ms. ( Icons- 1 to 1 correspondence where you can point and count). We also looked at partial icons (page 15 with the telephones) which are icons that show only part of the whole picture so it is sometimes harder to count. A different type of bar graph that we looked at was a stacked bar graph, which we are suppose to make with our M&M data that we organized on our bar graph sheet. Stacked bar graphs show part to whole. Grades 4-5 came up with a circle graph which shows each percent of color out of 100% We constructed a circle graph in our last AHE as well. Knowing how to construct and read these different types of graphs are crucial because you might be teaching a variety of grade levels so knowing which one to use is ideal.

Writing Assignment: DUE MONDAY, JANUARY 24th read BIAS handout Research Question- post on wikispace by SATURDAY NIGHT come up with what our target population should be and have it to discuss on MONDAY in class. tape M&M bar graph together to make a stacked bar graph
 * Homework: **

-This was really detailed and well written! Good job!.-Mallory Brownell -Good summary! -Paige Rodgerson Perfect! I like how you put what was due and when for homework! - Jaelei Ohrman

Lesson Two January 12

-//The Following mathematical ideas were the focus of todays class://

 * Idea 1:** We focused on the research question "Do math PSeT (preservice elementary teachers) think the same about teaching math to students?" Each group came up with three questions that could help us to find the answer to this question/problem. As a class, we chose to use a survey/questionnaire method to collect the data. We looked at each questions that the groups came up with, and discussed them in depth. We looked at what could be improved with the questions in order to make the data more helpful towards the problem question.
 * Idea 2:** When dealing with survey questions that collect data, we found that you must carefully state the question in order to obtain the desired answers you wish in order to help answer the problem question. This means to carefully choose the language to make sure it is clear for the reader. The questions should not be bias; for example, if you had a question that said 'What tools should be used in the classroom?', this can be classified as a bias question because you are assuming all classrooms need tools in order to learn math. Some questions may be better with an option to choose 'All of the Above', as it would make the outcome answers more clear to use towards the main research question. All of the questions we came up with can be looked at as the details to the main questions, where they can all be put together to answer it. Making sure the questions are relevant to the research question is a key component as well, because the more direct they are to answering the big question, the less questions you will have to have completed by the sample.
 * Idea 3:** The third big idea in todays class dealt with the AHE. Some small tasks that need to be completed are finishing the PIQ worksheet by hand to turn in next class (which will be Wednesday, due to no school on Monday). If you haven't entered you data on the Google Dox, do so now. Also, make sure you have entered a 'class norm' on this site. We have some homework, which is pg.13-20 that include marginal thoughts. Marginal thoughts are your own thoughts or notes that you come up with as you read, to be written in the margins of the pages. They can be questions, comments, or anything else you think that is related to the reading. Complete exploration on pg.21, and app. on pg.22-29 #1-4 (#1 use PIQ in the text on pg.9). *Use data on pg.30 when needed. We were provided with a package of M&M's to help with these assignments. All of this homework, as well as Monday's homework will be discussed on Wednesday as a class.

Lesson One January 10th The following mathematical ideas were the focus of today's class: There was an introduction to the class and how it will be run when we come. As a class we went through the steps of checking our TI-73 calculators to be sure that the software was up to date. We also learned the steps of hooking the calculators up to the hub so that we could all be connected for our in class work.
 * Idea 1- As a class we talked about different ways to get information. We used our calculators to take a poll of the question from our PIQ's about what simile best represented a math teacher in our opinion. We made predictions about what we thought the outcome would be.
 * Idea 2- As a class we were asked the question: How do we know we are doing statistics?
 * Idea 3- We came up with terms like collecting data, taking a poll, asking a question, using numerical data
 * Idea 4- We watched a video titled "Telling the Data Story". In the video we observed elementary classrooms in working with probability and statistics. The steps that the video showed the students going through while learning statistics were:
 * Collecting data
 * Organizing and Representing
 * Describing
 * Comparing
 * Summarizing
 * Analyzing Data
 * Predict Outcomes
 * =What we want to take away from the above ideas is:=
 * =Understanding what each step looked like as it pertains to probability and statistics, some of which we did not come up with as a class. We neglected the step of predicting outcomes, organizing and representing. It is important to note that statistics is more than just comparing numbers, or collecting information. There is so much more that students can learn when dealing with statistics, and this class is going to help us explore what that looks like=