Daily+Summary+of+Big+Ideas

I thought I had mentioned in class where the review session was but evidently not. Sorry. I have sent an email as well. It is Monday at 3pm on the 6th floor Alavi Commons in Everett Tower. Take the elevator all the way up, turn right and go all the way down at the end of the hall.

Announcement: Here is a website: [] that provides many graphs from USA Today newspaper. Click through and ask yourself questions similar to those from p 37 in the text. Keep this at top of page so it is easy to find. Test out this website! Really, you should view these graphs and test yourself as to type of graph and variable! Share your responses in class!! ==

_ Don't type above here!
Monday, April 19, 2010

Just as a reminder in case anyone forgot on monday we reviewed how to put a seed in our calculator using the home screen not the probsim app. We said you would enter the seed, then hit store after this go to MATH, PRB, and enter on rand. After this hit enter and the seed should be in the calculator. (Chelsey)

One big idea that we discussed in class today was a review of the Monte Carlo Method. We looked at the Racecar Rollie problem part e on page 179. To set up a simulation for the problem we could use numbers 1-100 to represent getting a ticket or not getting a ticket on the trip between Chicago and Detroit. Since the statistics show that 12% of people receive a ticket, numbers 1-12 would represent getting a ticket. Numbers 13-100 would represent not getting a ticket. We would use the randint function to generate one random number at a time. 10 numbers would represent 10 trips...this is a single trial. The probability of getting a ticket 5 or more times was found by adding the number of times a number from 1-12 was generated during the 10 trips. In our case, it happened 0 times so the probability is nearly impossible. (Jeannie) Wed. April 14, 2010

On Monday Dr. B will be giving a half hour of class time for our project but you must already come to class with some work done.

Big Ideas

Experimental probabilities - The outcomes over many trials of the experiment Theoretical probability -The relative frequency associated with a particular outcome tends to approach and stabilize at a specific value this is not a definition for theoretical probability. This still sounds more like experimental with a value stabilizing. This needs to be fixed! went over old homework Also discussed theoretical probability homework p. 176 #8 talked about the different outcomes for opened lines and closed lines. Than said The two equality likely outcomes of the line is opened or closed is modeled by choosing from two random numbers zero or one. Zero is opened and one is closed. A success is when both lines are open. Line one 1-5. and line two 1-6 More to the phone call problem than this! There were two stages. Notes are incomplete here. Please add more.

We worked on this again with problem number seven on page 176 What exactly did we work on? Didn't we discuss how to use tree diagrams? What about the area model? Please add more to these summary notes!

AHE - activity read p 184 - 186, complete p. 187 1-9, activity read p. 190-192 complete number one. Do at home quiz due on Monday. Dont forget that the project is due next wednesday:) (bailey)

Monday, April 11, 2010
 * Administrative stuff: we got our quizzes back; see Dr. Browning for specific questions. We can have a study group on Monday of final exam week but we have to pick the time. Someone in class needs to orchestrate that. We voted to have a take home quiz on probability. It will be due on Monday, 4/19. We can also switch groups if we want for the next two weeks.
 * Big ideas:**
 * Monte Carlo Procedure
 * Ways to "diagram" a probability problem
 * Programs to conduct lots of trials for better accuracy of experimental probability

Monte Carlo Procedure We selected several problems to discuss as a class but we only had time for 2: #1 and #6. Turns out they were very similar in structure. We referred to the MC procedure on p174, to write up the steps, particularly steps #1 and 2. We also need to complete steps #3 and 4 as those are based on the outcomes of our trials. We looked at how we could use the batter program on p 178 to model #1 on p 176. We only had to change the probability in the program from 45% to 50% for having a boy. We then compared that to #6 with the locks and found that problem to have a similar structure as well. How cool! Dr. B also presented a "tree diagram" to model the different steps in a probability problem, where each "stage" or step has branches related to the possible outcomes in a stage of the experiment. We started to make a tree for the family of 4 problem #1 p 176. The total possible outcomes in a family of 4 is 16 and we need to know how many have two boys. We need to complete that problem for homework.

We got our survey projects at the end of class. Again, if we have questions we need to make an appointment to see Dr B.

AHE: Actively read p 157-158 and completing p 159 #1-8. Actively Read 184-186; complete bottom of p 186. Make sure you finish all the Monte Carlo problems assigned on on April 7.

April 7, 2010 Today we discussed the outcomes of our "Star Trek" toy simulation. In this simulation we were trying to find the probability, or likelihood, of getting all six toys in just six boxes of fruit rollups. Since no one in our class got the six toys in six boxes, we found out that for the experiment conducted in our class, that outcome was impossible. we also discussed that even though we did not come up with this result, in theory someone could still get six toys in six boxes. this led us to realize that we had a very small amount of trials done for this experiment because there are only 16 people in our class.

This led us to ask " how many trials is enough?" We started talking about this when the question " how many trials would NASA need to do before sending people up into space?" We never came up with a specific number but decided that the more trials you do in a simulation, the more comfortable you feel about the outcomes.


 * We must always remember that when giving a probability, the number comes out as less than one because the probability is part to whole, with one being certain and zero being impossible

EX: when we were doing the trials for the star trek toys, the trial was defined as the amount of boxes bought to get one of each of the toys for the birthday problem ( when asking 5 people their b-day month, what is the probability of two of those 5 people will have the same birth month) the trial was defined as asking 5 people what his or her birth month was Calculator stuff: If you had a dim- mismatch come up on you calculator, there is something wrong with your list, check 2nd plot and fix it
 * Remember that the trial is determined by the outcome....

AHE: actively read Pg: 174
 * 1) 1-9 Pg: 176

April 5, 2010 Random**: when we know what could happen, but it is uncertain what we will get as a result. EX: Tossing a coin could happen: heads or tails (with a fair coin) equally likely: 50/50 chance (50% chance) EX: Spinner could happen: 4 outcomes does not necessarily have to be equally likely (some sections could be larger or smaller than others) EX: Hershey kiss toss could happen: tip up/tip down not equally likely

-In the long run, (coins) we expect to have 50% heads and 50% tails. -In general, in the long run, we can make predictions -We connected working with fractions and probability

P. 142 Red = 2/3 = 8/12 White = 1/4 = 3/12 Blue = 1/12 -on the first spin, you could get red, white or blue -red is most likely because the area was larger, but white and blue are always possibilities too EX: I spin B,W,B,W what are my chances of getting red? the probability is still the same as the first spin because the spinner is fair and still random as any other spin

P. 143 #3 On what information do you think each of the stated probability was based a. data collected, fronts coming in, its raining on b. how many tickets were printed, one winner**

Trial**-one run/test/sequence

P. 151 Hershey Kiss Data Total points up: 30 + 37 + 31 +42 + 36 = 176 Probability of getting point up number of points up/total trials = 176/500 = 35.2%**

Outcome of interest**: event example: kiss landing point up, tossing a die

PROB SIM "set" "trial set": 1 "coins": 1 "graph": Freq "cleartbl": yes "update" "Adv" __side wght prob__ tails 1 .5 heads 1 .5 tails 81 .648 heads 44 .352
 * change prob

press "ok" not "esc"

P. 153 #4b Event: You will pick a green or yell M&M (outcome of interest) Experiment: Open a package of M&Ms and randomly select a single candy 869/3082 about .28 or about 28.20%

P. 155 #8b (A)=male (B)=ticket i. p(A)=12/20 ii. p(B)=11/20 iii. p(A&B)=8/20 iv. p(A or B)=15/20

AHE p. 152-156 #1-9 (skip 2) p. 166 p.167 use our data for #1

​**March 30, 2010 On a line graph the x-axis = time x-axis=Independent=Predictor y--axis=Dependent=Predicted The y-axis depends on the x-axis.

Ways to show continuum:
 * 0-1
 * 0%-100%
 * Thumbs up, down, sideways
 * animals that you would normally see and animals you would not normally see

On page 141 How likely is it that a random person in our class will sleep with socks on? Representativeness and availability cloud our judgement
 * Likely, not likely, in the middle (maybe/might)?
 * 3/16 of our class sleeps with socks on which is equal to 19%
 * 3/16=19%=.19

You can use fractions, percents or decimal on a continuum. Sometimes you may want to use fractions while other times you may want to use percents

As a class we defined random This is our first definition: A random event is when there is no distinctive pattern, out of the normal, no preference, irregular, uncertain, we know possible outcomes. As a class we tweaked this definition and rearranged it until we got our final definition: A random outcome is when we know what could happen but it is uncertain as to what we will get at a particular given time.

We also learned how to generate random outcomes on the calculator:
 * Math
 * -> PRB
 * #2 RandInt(
 * <span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif;">RandInt(smallest number, big number
 * <span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif;">Enter
 * <span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif;">Example RandInt(0,1) will randomly give you a 0 or 1.

<span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif;">To <span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif; text-decoration: line-through;">be generate <span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif;">random numbers <span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif;">in a list
 * <span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif;">Be in a blank list (list with header but no data in the list)
 * <span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif;">Math -->
 * <span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif;">PRB #2 (RandInt
 * <span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif;">(smallest, largest, how many times)
 * <span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif;">enter
 * <span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif;">Example: RandInt(0,1,50) will randomly pick 0 or 1 50 times in the list.

<span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif;">Theoretical Probability Vs. Experimental Probabilty
 * <span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif;">Theoretical: Example: On a coin you have two possible outcomes (heads and tails) the theoretical <span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif; text-decoration: line-through;">probabily probability <span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif;">would be 1/2 Heads and 1/2 Tails describe this in a general way as well. What makes what is written here theoretical??
 * <span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif;">Experimental probability<span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif;">: Physically doing an<span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif;"> experiment <span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif; text-decoration: line-through;">and counting the outcomes to find the probability estimates.

<span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif;">We have an application on our calculators that will randomly spin a spinner, flip a coin, and a few other random activities. <span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif;">When you flip a coin it has equally likely outcomes When you roll a chocolate kiss the outcome is not equally likely
 * <span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif;">apps
 * <span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif;">Probsims
 * <span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif;">hit any key
 * <span style="color: #18abe2; font-family: Verdana,Geneva,sans-serif;">choose an activity

Homework: Take home quiz due next Wednesday Read p. 140-141 P. 142 #1-4 P. 152 #1,3-9 odd

<span style="color: #8a08c9; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">March 29, 2010
<span style="color: #8a08c9; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">ANNOUNCEMENT: Projects are now due on friday at noon at the MAIN MATH OFFICE, not Dr. B's door!!

Mean and Median Exploration

mean is a "center" but that does not mean that it is right smack dab in the middle of the data values
 * <span style="color: #8a08c9; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">Balancing: mean is balancing all distances of the data values from the mean so the sum of the distances is equal on both sides of the mean
 * <span style="color: #8a08c9; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">middle: median always sits in the middle of all values
 * <span style="color: #8a08c9; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">median is greatly affected when a point in the middle is moved up and down the number line because the median always has to stay right in the middle of all data points
 * <span style="color: #8a08c9; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">the mean <span style="color: #8a08c9; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; text-decoration: line-through;">drastically <span style="color: #8a08c9; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;"> changes when upper or lower extremes (especially outliers) are moved up and down the number line.
 * <span style="color: #8a08c9; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">the mean <span style="color: #8a08c9; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; text-decoration: line-through;">drastically <span style="color: #8a08c9; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;"> changes when upper or lower extremes (especially outliers) are moved up and down the number line.

The changes in the mean can be dramatic when the extreme values are outliers

 * <span style="color: #8a08c9; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">spread and distribution are changed when upper and lower extremes are changed -- measure of spread = range

Scatter Plots<span style="color: #8a08c9; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;"> y-axis is dependent variable what is happening??**
 * x-axis is independent variable

COMPLETENESS & CLARITY:
 * <span style="color: #8a08c9; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">positive association
 * <span style="color: #8a08c9; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">if we put a line through the scatter plot, all points would be scattered around the line
 * <span style="color: #8a08c9; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">the number of deaths increases as the number of cigarettes smoked increases
 * -You could draw a trend line along the clustered points that would show the associations of the data points. Since this is a positive association, as independent variable increases, the dependent increases as well

Lurking Variables: this means there are other variables that could be affecting a certain association -- does the number of people per television //really// affect the life expectancy in a country?? NO-- there are other relations that could tie these two together like poverty, health-care, and resources.**

"Teaching Math" K-4
 * probability terms: probably, chance, experiment, impossible, certain, predict

two ends of probability:** impossible ---not likely--maybe--likely--- certain 0% 100% 0 1, 1/1, 1.0

Thinking like a teacher: What visuals would help students understand this continuum?

AHE:<span style="color: #8a08c9; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;"> p. 87 # 1-4 define: "randomness"** READ BY BAILEY:)
 * p. 83 #8, #10

Hey everyone this is jenny.... sorry for not posting this earlier but the missing data for money spent on book is $301-400.

March 25

in class we talked about a new way (this shouldn't be too new since it was in your homework!!) to find the SD on your claculator.. you first hit second stat, then scroll over to the "calc" menu and then hit the first option you then pick what you want to find the SD off. the standard deviation in this program looks like this o~X.

We then started talking about Cat Cat, Num Num and Cat Num graphs. We said that a stem and leaf graph would be a Cat Num graph. It could possibly be however, you don't really see the data on a simultaneous display; the values are still side by side. So a stem & leaf is a much better COMPARATIVE display rather than one looking for associations as in the Cat Num.

Next, we talked about what "associations" mean. We said that associations is when there are 2 things that are interlocked interwoven. that if you know something about 1 thing you can predict something on the other thing. We then discussed associations between NUM NUM graphs preferably our Ht and Arm data. We made a dot plot scatter plot of this information. we discussed which variable goes on the vertical line axis and which variable goes on the horizontal axis, there are 2 names to this, independent and dependent variables. We came to the conclusion that the independent variables, ones that stand alone and are not influenced by the other, goes on the horizontal axis. the dependent variable depends on the independent varibale and is located on the vertical axis.

We then discussed directions of lines the associations. if a line is going from bottom left to upper right then it is considered a positive association. if the line goes from top left corner to the bottom right corner then this is considered a negative association and lastly if the line data is all over the place with no direction then this is considered a scattered direction. apparent clustering along a line, then the data is said to have no association.

we then made a scatter plot on our calculators and then fit a line on our calculators. to make a line you: 0. In mode, fix the numerical display to 2 decimal places. 1. Go to your gaph 2. hit 2nd stat 3. go to manual fit 4. there should be a blinking cursor on your graph 5. find where your arrow would go if you were to draw a line Move this cursor to begin to form your line of fit. Typically, you will head for "extremes" on the display, such as lower left and upper right. Once at an extreme, you press enter to lock a point on your line of fit. Then move to the other extreme; while you are moving there, you should notice a line of fit appearing. Once you have chosen your second point, press enter to fix the line. 6. hit enter 7. once you hit enter a second time an equation for your line of fit will pop up. 8.DONT HIT ENTER AGAIN.. or the equation will go away the equation will be in the form of y = mx + b, for example shoule be something like Y=.69x+51.25. your .69 x is your slope and your 51.25 is your y intercept if you hit your right arrow this will change your Y intercept; scatter you can adjust this equation by using the arrow keys. When you are satisfied with the line of fit you have made, you have two choices to keep this equation. #1, write it down on a piece of paper or follow the next set of instructions. The equation you have will disappear once you hit enter to stop the Manual Fit process. If you lose your equation you: 1. go to Y= 2. 2nd varrs 3. go to the option 3 stats 4. arrow to Eq 5. choose regression

We then talked about slope being rise over run. Why did we talk about this? Where is AHE??

March 22, 2010

We started class by going over the difference between S.D. procedure and S.D. conception. >S.D. Procedure: Find the sum of the data, find all distances away from the mean, square the amounts, find the mean of all squared distances (variance), square root variance. >S.D. Conceptually: spread of the data away from the mean, looking at the mean average of distances from the mean.

We also discussed that if the S.D. is smaller, the data will be a small distance from the mean.

We went over homework problem #4 on pg.133 >1 S.D. is equal to the square root of the variance >we found that in this case, 1 S.D. is equal to 10 values away from the mean. >the S.D for 108 is 3/10 S.D. because it is 3 out of 10 values away from the mean. We also found that z-score can be equal to 0. >x=mean; mean-mean

We then looked at our charts tables on pg. 67 >We concluded that the first table is a Comparison because it only has 1 variable. Careful, does it just show one variable? If so, what is the single variable? If not, how many variables are there? >>Ex. 1 more right-thumbed person than left-thumbed >>More dominant right-eyed people than left-eyed. >The second chart is an association chart because it compares 2 variables at 1 time. Not just at one time but simultaneously **.** >>We made stacked bar graphs to represent the association between the variables. >>>Percents of the whole are used to determine the amounts for the stacked bar graph.

We finished up with discussing the different types of association. >CAT-CAT association: two categorical data sets. Nice for 2x2 or 3x2 data sets. >NUM-NUM association:two numerical data sets. >CAT-NUM association: one categorical and one numerical data set.

Homework: >pg. 136 #2, 4, 5 >pg. 68 fill in the graphs >pg. 69 #1 and 2

March 17, 2010 We began class today by looking at standard deviation, so far we have only looked at single variables. We then looked at page 121 and took a quick poll with 90,67,60 as our choices. We then discussed how we got all the different numbers in the polls. Colleen then explained this particular problem on pg 121 and we then subdivided into groups to show how we got the upper extreme the median and the lower extreme. We then moved on into the ages of the presidents deciding whether or not the ages should be a whole number. The class came to an agreement that whole numbers would be best suited for the presidents ages. After this discussion we then got into a discussion on the median in this particular data set. Since there are 35 numbers in this set of data you add one to 35 to give you 36 and then divide by 2 to give you 18. The 18th number is the median of that particular set. We then discussed what the value of the lower quartile meant and we came to a class agreement that this is a point of our box and whisker plot that is the median of the lower half. After we discussed pg. 121 we then moved to page 118. On pg 118 We discussed Fair Share and Equalizer Idea and we took what we learned from the mean and applied it to pg. 121 Since 68.8 was our average of all our data on pg. 121 we can't just add in 2 more presidents and divide by 3. We still need to find our equalizer with the 2 added presidents so by using the balance approach we have to recalculate our data with the 2 new presidents added. After this problem we moved on to page 124 number 4. We then entered 25 scores into the calculator. And agreed that outliers are separated widely from the rest of the data. We then made a box plot sketch that sits above the line. We then went back over the lower extreme and what it represents and we came to the conclusion that the lower extreme is 1 in a half interquartile ranges away from the lower quartile.

Hwk pg.132 1-6 7,8

March 10, 2010 We began class today by a continuation on the discussion of mean, median, and mode. We discussed that, when giving an "average" number, one could mean either the mean, median, or mode. The "mean" number being described as the number you get after adding up and of the numbers in a data set and then dividing that number by the amount of numbers in the data set. The "median" number begin described as the middle number in the data set, and "mode" being described as the most occurring number in a data set. We then discussed a homework problem that made us find the mean, median, and mode of a set of numbers after finding the last 2 numbers and following a strict set of guidelines. We also discussed what the range of a set of numbers is, which is the minimum number to the maximum number given in the set of numbers. We next discussed how to begin to make a dot plot. It was said that we must first determine the scale and distinguish between a large or small scale, which can be determined through the min and max numbers. You then find the median number, which means that there is half the data on side and half the data on the other. You can look more closely into each half by finding the median number of each side. To find half of one the halves, you can just apply Daveys method (all the numbers plus 1 then divided by 2). In class today, we also discussed box and whisker plots. We discovered that any number that is beyond 1.5 interquartile range is called an outlier. The range is based on min and max and the spread is based on the median. AHE: Study for the test on monday!

<span style="color: #ff00ff; font-family: 'Comic Sans MS',cursive;">March 8, 2010

In class today....

The very first thing we did in class was resend our arm and height data but we also sent our shoe length through navnet and created new lists for them.

We then began looking over homework problems. We started by going over the "George" problem on page 99. We determined that George found the mean using the fairshare method.

We were told that if given the word MEAN, we hope the word said would not be average because the mode and median are also kinds of averages.

We were trying to determine if the dot plot on p. 99 was a good representation of the cube towers George made of the data. As a class we came to the conclusion that yes, even though the dot plot and cube towers do not look the same, or similar at all they are both representing the same data. After taking a poll, almost everyone determined the same thing, that yes, both graphs were representations of the same data.

We then went to the worksheet we had for homework titled: "What Happens If...." the worksheet gave us a group of numbers in which we had to answer the following quesions. The numbers were: 1, 1, 2, 2, 2, 2, 3, 3, 4, 5.

We started on problem A which asked us to determine the mean of the numbers. After using a balance, fairshare, and equalizer examples we determined that the mean was 2.5. We then moved on to problem C which asked us if we added another 2 to the data what would happen to our mean? We determined that the mean would go down because if we added a number to the data taht was less then the mean it must go down. For example: if we put these numbers in cube or bars and added another cube or bar, in order to make them all equal (fairshare) we would have to take a little from each bar/cube in order to make them all equal which means the mean would go down.

We then began doing calculator work. We discovered that if you had a list of numbers in which you wanted to determine the mean, but you add, or multiply the numbers in the list by another number the mean would just be added or multiplied by the same number.

We then worked on a group problem on p. 105 #3 and half the class used a bar graph to determine the answer and the other half of the class used the table that was given along with the problem. The big idea that we got from this problem was that the word VALUE is usually attached with a number or numbers, but we discovered it doesnt always have to be. A value could be a category as well.

AHE: Actively read p. 117 Work through and complete first exploration #1 P. 121 problems 1-8 Read and Complete P.127 <span style="color: #8a08c9; font-family: 'Comic Sans MS',cursive;">Read by: Bailey waterhouse:)

Day 13 Feb 24, 2010

In class today we talked about how we are starting to focus on the little s in statistcs.

We talked about mean there is fair share equalizer - where you put a line on the bar graph to find the mean balance - The balance of the mean does not always have to be in the middle

The next thing we did was go over our project - Make sure you talk to Dr. Browning if you're having a problem with your paper. Make sure you're making yourself clear on all parts of the project. She will be more than willing to look over your project again for you.

We than worked on problem #6 p. 101 - looked at the equalizer p. 103 - looked at table 2.1.1

Evenly distrubition means flat data.

The difference between the mean and median. The mean is the average number (LET'S THINK OF A DIFFERENT WORD HERE OTHER THAN AVERAGE; THE MEDIAN IS AN AVERAGE, TOO!) while the median in the middle number. We also talked about how your average would be more messed up if you added an extream number. This would be more affected more than your median.

AHE - worksheet - What happeneds if....? P. 106, # 2 - ​14, 19

<span style="color: #000080; font-family: Verdana,Geneva,sans-serif;">Day 12 Feb 22, 2010
<span style="color: #ff0000; font-family: Verdana,Geneva,sans-serif;"> p.99 Applications We then broke up all the towers and divided them back up into seven towers making each tower equal in height. This is how we found our mean. We were able to divide the towers up equally because 28 can be evenly divided by 7. Other groups just starting moving blocks around until all towers were the same height. We had two different approaches. <span style="color: #ff0000; font-family: Verdana,Geneva,sans-serif;"> We discussed that the Average is NOT the same as the mean. The Average can equal the: mean, median, and mode. Mean: add all together and divide.
 * 1) 1- We discussed how to find the median, mode and mean. We found the median by ordering the towers up from smallest to largest. After that we found which tower was in the middle and that was our median. We found that the tower that occurred the most was was six which would be our mode.

<span style="color: #000000; font-family: Verdana,Geneva,sans-serif;">Is this the only conception we have for mean? I'd almost like us to forget this one for awhile and focus on the others we have developed. Please include those conceptions for mean here and save the procedural one for the last one!

<span style="color: #ff0000; font-family: Verdana,Geneva,sans-serif;">Mode: Number that occurs the most frequently. Median: The middle number.

We talked about how the mean can balance the data set. The distance from the balance point would equal the mean. This distance must be equal. Are we sure about that?

<span style="color: #ff0000; font-family: Verdana,Geneva,sans-serif;">p. 101 #9 Finding the Average using a balance approach. 1.) Order them 2.) Find the middle of the balance. Is the fulcrum always in the middle? Think about the "delta" problem we did in class. <span style="color: #ff0000; font-family: Verdana,Geneva,sans-serif;">3.) Find the distance

Finding the average using the Algebraic approach... I'd call this the fair share approach. <span style="color: #1d5f8c; font-family: Verdana,Geneva,sans-serif;">(161+142+145+149+x)= 147 5 (161+142+145+149+x)= 147(5)

597+x= 735

735-597= 138

x= 138

AHE: Actively read p.102, complete p.106 #2 Done by: Chelsey

p. 52
We discussed the importance of making sure all the numbers are aligned vertically in a stem and leaf plot so that the lines are not deceiving. We also saw the differences between stem and leaf plots and dot plots and how they can appear very different when looking for clumps bumps and holes.


 * stem and leaf: goes up by tens so clumps are not as defined
 * dot plot: can see individual spaces and the actual distribution of frequencies
 * mode, mean, and range are visible in both sets
 * if there is data in the thousands, histogram is best
 * or, if there is a lot of data, put dots between each line and it gives two lines per stem to avoid stringing out the lines
 * frequency distribution=a histogram

p. 63 #4
a. choice a is the research paper because there are bigger words -- USA today probably uses smaller words so that more of the population can actually understand it --this can be a good exercise for students because they can collect data by simply counting the letters in words --ex: comparing the sizes of words in different level science text books b. fifth grader Adam is focusing on the spread and appearance of the graphs rather than the mathematical data --he is struggling with how to actually read the graph -- it is a very common mistake to just look at the graph rather than actually analyzing it and reading the data

p. 97 #1

 * we used cubes to make bars to find what an average or typical size family is
 * there are different ways to order the bars: shortest to tallest, fair share, great big tower stack them all together
 * we learned a new symbol the sigma: ∑
 * ∑x is the sum of all values together
 * ∑x over //n// is a way to find the mean or x bar

"AVERAGE"
There are different ways to find the average of something, average does not always mean to add up all the numbers and divide.


 * median: find the middle number
 * mode: find the number that occurred the most in the data
 * "The average teacher is female" >>didn't add up all the teachers and divide, just found the most frequent
 * mean: find the fair share of all of the numbers, balancing point

Day 10 Feb 15, 2010
Review of Past Big Ideas
 * Types of Graphs (Numerical and Categorical)
 * Numerical
 * Stem and leaf
 * Dot plot
 * Can see individual outcomes with numerical grapghs
 * Range-statistic measure. It is the different between the highest and lowest value. Range is a measure of the spread of the data
 * Variability-another way of looking at the distribution of data
 * Outcomes can be ordered
 * Other things we can look at with numeric data
 * Clumps-clustering of data
 * Bumps-mode, highest peak
 * Holes-gaps in the data with no outcomes
 * Questioning
 * Read-answer can simply be read from display
 * Derive-some type of computation is necessary
 * Interpret-thinking goes beyond data
 * These are on a continuum and some may blend into each other
 * Percents
 * When comparing, must be out of the same whole

New Big Ideas ​Day 9 Feb 10
 * Looking at the shape of data
 * Symmetic-appears the same on both sides of a reflective line
 * Skewed-values are clustered near one end of the data with some value(s) pulling display toward the other end. See page 61 for an example for a skewed display
 * Histograms
 * Looked at handedness ratio
 * Xscale is refered to as bucket width
 * Window-should have a "mat" around the graph like a frame around a picture
 * May be helpful to use -1 or -2 for a ymin value so that the trace information will not be covering the display on the calc
 * To sort a list: from the home screen (a blank screen) hit 2nd stat, then go to ops, choose to sortA(ascending order), hit 2nd stat, select list to sort. The values in the list column will now be ordered.
 * The xvalues displayed include up to that number but not that number itself in the bar to the left of the value.
 * Mystery Balancers
 * We decided with some debate
 * A-karate students
 * B-first and second graders
 * C-gymnasts
 * D-people over 50
 * Must be able to rationally explain why you believe each to be which group.
 * AHE
 * Project part 1 due Wednesday
 * read page 55
 * complete page 62 #3,4,5
 * actively read page 96
 * complete page 97 #1,2
 * Homework problems we did not get to
 * page 58 #1b
 * page 65 #1

<span style="color: #008080; font-family: Georgia,serif;">REMEMBER: Frequency is NOT the data!!! Frequency is the count of the outcomes of the variable <span style="color: #800080; font-family: Georgia,serif;">

<span style="color: #4e37b3; font-family: Georgia,serif;">Looking at the Pulse graphs: **

<span style="color: #31d851; font-family: Georgia,serif;">Dot plot is preferred to show numerical data WHEN DATA SET IS SMALL because it shows individuals When graphing the scale must always be the same, you cannot increase by 1 each unit and suddenly start going up by 10's of 15's by the same unit.
 * <span style="color: #4e37b3; font-family: Georgia,serif;">Displays categorical data
 * <span style="color: #4e37b3; font-family: Georgia,serif;">graphs to display categorical data: real, picture, bar, circle, stacked bar
 * <span style="color: #4e37b3; font-family: Georgia,serif;">Is ordering categorical outcomes necessary?
 * <span style="color: #4e37b3; font-family: Georgia,serif;">No-> does it matter how you organize what type of pets you have? Does hair color need to go in a certain order when graphing? Nope.
 * <span style="color: #4e37b3; font-family: Georgia,serif;">Graph 1:
 * <span style="color: #4e37b3; font-family: Georgia,serif;">uneven spacing on the vertical axis (Ex. space between 2 and 3 is half the size as the space between 3 and 4)
 * <span style="color: #4e37b3; font-family: Georgia,serif;">Vertical axis starts at 0 and horizontal starts at 50, could use W (squiggle) on the line to show nothing before than (gap)
 * <span style="color: #4e37b3; font-family: Georgia,serif;">gaps between bars on the horizontal could be confusing
 * <span style="color: #4e37b3; font-family: Georgia,serif;">The scale on the horizontal is uneven (50-55 and 56-60)
 * <span style="color: #4e37b3; font-family: Georgia,serif;">Graph 2:
 * <span style="color: #4e37b3; font-family: Georgia,serif;">Random numbers on horizontal
 * <span style="color: #4e37b3; font-family: Georgia,serif;">same data used for horizontal and vertical
 * <span style="color: #4e37b3; font-family: Georgia,serif;">The vertical axis is not labeled
 * <span style="color: #4e37b3; font-family: Georgia,serif;">Graph 3:
 * <span style="color: #4e37b3; font-family: Georgia,serif;">horizontal is slightly confusing, if you didn't know how many students total it could be easily mistaken for multiple students per line instead of it being a student id number
 * <span style="color: #4e37b3; font-family: Georgia,serif;">Graph 4:
 * <span style="color: #4e37b3; font-family: Georgia,serif;">confusing, start at 50
 * <span style="color: #4e37b3; font-family: Georgia,serif;">data spread out because they are not in categories
 * <span style="color: #4e37b3; font-family: Georgia,serif;">advantage for younger students
 * <span style="color: #4e37b3; font-family: Georgia,serif;">could find yourself
 * <span style="color: #4e37b3; font-family: Georgia,serif;">is the hole box even and line odd?
 * <span style="color: #4e37b3; font-family: Georgia,serif;">Dot plot
 * <span style="color: #4e37b3; font-family: Georgia,serif;">Last Graph:
 * <span style="color: #4e37b3; font-family: Georgia,serif;">Similar to graph 4
 * <span style="color: #4e37b3; font-family: Georgia,serif;">Smallest to the largest
 * <span style="color: #4e37b3; font-family: Georgia,serif;">Individuals

<span style="color: #ff00ff; font-family: Georgia,serif;">Vocab:


 * <span style="color: #ff00ff; font-family: Georgia,serif;">Intervals= Scale
 * <span style="color: #ff00ff; font-family: Georgia,serif;">Range= Spread of the data
 * <span style="color: #ff00ff; font-family: Georgia,serif;">Smallest to largest number
 * <span style="color: #ff00ff; font-family: Georgia,serif;">Range is a single number
 * <span style="color: #ff00ff; font-family: Georgia,serif;">Another word for spread is __Variability.__ Range is one measure of spread.
 * <span style="color: #ff00ff; font-family: Georgia,serif;">Clustering/Clumps- On dot plot where data is clustered together
 * <span style="color: #ff00ff; font-family: Georgia,serif;">Gaps/Holes- Gaps in data (Ex. No data 80-85)
 * <span style="color: #ff00ff; font-family: Georgia,serif;">Bumps/Mode- Data goes up. Typically the highest peak on a graph is our bump, however, some people would see more than one bump. Ex. Graph 1: If you roughly run your pencil on top you would see a bump at 71-75 and some would see another at 86-90
 * <span style="color: #ff00ff; font-family: Georgia,serif;">Distribution- How is the data spread throughout the display?
 * <span style="color: #ff00ff; font-family: Georgia,serif;">Variability is the spread of the data and is a key feature in describing a distribution (p. 48)

<span style="color: #0099ff; font-family: Georgia,serif;">We reviewed stem and leaf graphing, go back to page 44 to review

On page 52 when doing the stem and leaf graph increase as moving away from the middle.

<span style="color: #e78023; font-family: Georgia,serif;">AHE:


 * <span style="color: #e78023; font-family: Georgia,serif;">Reminder: Part 1 of the project is due next week (18th)
 * <span style="color: #e78023; font-family: Georgia,serif;">Reminder: Quiz Feb. 22nd
 * <span style="color: #e78023; font-family: Georgia,serif;">Read p. 41-45 actively
 * <span style="color: #e78023; font-family: Georgia,serif;">p. 51 #6-8
 * <span style="color: #e78023; font-family: Georgia,serif;">Complete histograms: Read p. 55-56 Actively
 * <span style="color: #e78023; font-family: Georgia,serif;">Complete exploration: p.56-57 p. 58-60 #1

<span style="color: #0ea031; font-family: Georgia,serif;">Old Homework Problems we went over in class Page 48 #1


 * <span style="color: #0ea031; font-family: Georgia,serif;">Used Numerical and Categorical data on the dot plot\

<span style="color: #0ea031; font-family: Georgia,serif;">Page 48 #2:


 * <span style="color: #0ea031; font-family: Georgia,serif;">Turned Categorical data into Numerical data
 * <span style="color: #0ea031; font-family: Georgia,serif;">Range= 1-12
 * <span style="color: #0ea031; font-family: Georgia,serif;">How do you look at clusters of data?
 * <span style="color: #0ea031; font-family: Georgia,serif;">Large groups of data with a drop in data on both sides
 * <span style="color: #0ea031; font-family: Georgia,serif;">Look at frequency
 * <span style="color: #0ea031; font-family: Georgia,serif;">Bump/Mode= 3 (It is important that things line up so you can see bumps)
 * <span style="color: #0ea031; font-family: Georgia,serif;">Gap/Hole= None-> All months have at least one person's birthday

Day 8 Feb 8th 2010
Survey Project Move around campus more go to different buildings don't just survey your friends Large Scale- made large to show detail > Small Scale- a relatively small representation of something, usually missing out details
 * Random Sampling
 * Random Sampling
 * What is Scale Clairification
 * What is Scale Clairification
 * Send Dr. B an email about scale definition
 * Read, Derive, and Interpret Questions
 * Read, Derive, and Interpret Questions

Homework review page 34 #2 > Examples of the different questions could be: > Read: in 1999 what percent of the 5th graders scored in the novice level in science? > Derive: in 1999 how many of the 5th graders scored in the novice level in science? > Interpret: Do you think that the score of the 5th graders could be inmproved in 2000, if so how and if not why? > Carefully check questions to make sure you know what they are asking and if they can even be answered at all > A derive question can be defined as a question that needs some computation with the information from the table or graph provided to answer Percents are reletive frequencies > one cannot always directly compare percents > we must make sure that the two percents have the same whole to compare them other wise the comparison wouldn't be acurate > > Homework: worksheet passed out in class, page 48-54 numbers 1,2,4,5,9 (for number two add our data we collected in class) > =Session 7 Feb 3=
 * Read Vs. Derive
 * A read question can be defined as a question that can be answered by "reading" the table or graph provided with the question
 * Percents
 * We began the day by creating three lists of numerical data on our calculators, these lists represented Height, Wingspan, and Pulse Rate. We gave them labels of L1, L2, and L3.
 * Our next task was to rename these lists. (just like the "Save As" function on your computer.) We did this by substituting the information into the table under new names.
 * Next, we focused on our pilot survey results, and came to the simple conclusion that in any statistical analysis, the samples must represent our population.
 * Our conclusions upon looking at all the data combined, was that we need to survey more lower underclassman, as well as a larger variety of students from the different colleges on campus.
 * We then began discussing question 7-b on page 39 of our text. We came to the conclusion that the issue of the question was that none of the examples worked with the graph. These are some of the reason why,
 * Each section on the graph is its own 100%, therefor we cannot answer any questions that ask us to combine the totals from different parts of the graph.
 * We could not answer question 4, because we do not know the "of what" factor. This meaning that we can answer with a number, but we will not be able to tell what that number represents.
 * Near the end of class, we discussed the advantages and disadvantages of a set of displays we were given. The most common problems involved confusing labels and the need for a better scale.
 * The problems on the board that we didn't get to were Pg. 35, #1-a and 1-c, and Pg. 34, #2

<span style="font-family: verdana,arial,helvetica,sans-serif;">Have your comments on the pulse graphs ready for Monday

 * For Weds

which one is larger scale??? Calculator stuff:


 * When wanting to see the categorical information when using your calculator, hit the trace and see the categoires with their info at the bottom
 * Make sure when graphing that the other plots that you are not using are turned off before graphing.
 * When you go into your plot application on your calcutalor, if you hit the nuber 4 button and then hit enter, it will turn off all of your plots

AHE:


 * 1) Make sure to print off the survey questions that were emailed to you by DR. B
 * 2) Have 2 people complete the survey before weds.
 * 3) Pg: 35 # 1-8

Bailey Waterhouse //required// //and text books// Reminder for Survey Project As a class we discussed... 1. Who is our population? - full time undergrad students at WMU 2. All students who: take classes at WMU Then, we took a vote to see which option would be our population and the results were... 1. 1 person 2. 7 people 3. 4 people So, we decided that our survey population would be all WMU full-time undergrad students who: are required to buy books/materials. Then, at the end of class, we discussed our Eye Color Data. We said that this data would be categorical. When looking at any data, always ask, "What is the whole?" We looked at all different types of graphs that the class made and said that... Circle graph: it is a sample of our class and looking at the data, it refers to the part-to-whole concept Bar graph: unlike the circle graph, you cannot directly read the portion, you can only see the frequency. Portions can be computed from the frequency data. We looked at our data to figure out the exact percentage of the brown eye color. Brown - 8/17 = .47 --> ~47.06% (symbol) can't do anything with this! 8 is the number of people with the eye color brown 17 is the total number of people in our class We concluded that instead of saying 47%, we would display our results accurate to two decimal places and would use 47.06%. This is still an approximation and NOT an exact answer. __AHE__ Quiz on Monday!! Read page 32-33 Answer page 34 Do page 35, 1-8 Look over Survey Questions Get the correct height/arm span measurement if you have not done so all ready Day 3: Jan 20 <span style="color: #da00ff; font-family: 'Lucida Console',Monaco,monospace;">Today in class we revised our survey question to the following: What is the cost of required materials on campus bookstores per semester? Data to consider for survey:
 * Make sure to look over rubric carefully and ask Dr. B for more clarification if needed!

How many //classes// students are enrolled //credits//

<span style="color: #da00ff; font-family: 'Lucida Console',Monaco,monospace;">Population of survey to consider:

Full time/part time student

<span style="color: #0000ff; font-family: 'Courier New',Courier,monospace;">__Categorical Variable__- (only one answer) outcomes are non-numeric, groups or categories __Numerical Variable__- (can have both answers-categorical & numerical) measurement*, count __Count variable__- thought of as a subset of the measurement vairable __Frequency__- how many of the data Also working towards determining what graphical displays are appropriate for what type of data and examining graphs we made last week to determine appropriate methods for constructing the graphs. __AHE__<span style="color: #0000ff; font-family: 'Courier New',Courier,monospace;"> Ask 3 before me! (check w/group mates on any homework question before asking Dr. B) Don't wait to state you're behind when following a calculator activity. Wiki-post survey question for either Categorical or Numerical as assigned by Dr. B Wiki Definition page-post one word w/definition from Math 2650 (one person from group) Wiki - allow email notification in the Manage Wiki section. P. 22-29 #1 - 4 READ CAREFULLY! READ IT AGAIN. P. 30 when you need M&M data from the class __Research: Survey:__
 * //If// it can be a "partial", ex: 1 1/2 or 20 yrs + 3 mo., its measurement!







__real graph__ __picture graph__

__skip count__



__Eye Color Data Day One: Jan 11__ // Today in class we discussed // the question " What is Statistics?" The class came up with, Statistics are:

the gathering of information

> > We then put these ideas in order. The class came up with > > We then watched a video called " Data Story" which explained the steps of statistics. The steps that were explained in the video were: > > formulating a question > AHE: create a question we could investigate then email that to Dr. Browning. Read pg 1-4 and 10-12. Do #1, 2-5
 * following, prediction, and discovering
 * trend ( following a repeated pattern)
 * using graphs ( being organized)
 * helps interpret large groups of data
 * using graphs ( being organized)
 * helps interpret large groups of data
 * helps interpret large groups of data
 * helps interpret large groups of data
 * trend
 * helps interpret large groups of data
 * gathering of information
 * using graphs (being organized)
 * Summarizing
 * gathering of information
 * using graphs (being organized)
 * Summarizing
 * using graphs (being organized)
 * Summarizing
 * Summarizing
 * collecting data
 * organizing and representing
 * describing, analyzing data
 * comparing
 * summarizing
 * describing, analyzing data
 * comparing
 * summarizing
 * summarizing
 * summarizing