1. Shoe Size  Please write your shoe size on the board.  Girls put yours on the girl’s chart  Boys put yours on the boy’s chart

2. And Customized Shoes

3. 10 15 20 25 Number of items recalled Non-caffeine Caffeine A study of the effects of caffeine on memory recall was conducted. Volunteers were asked to take a memory test 2 hours after either drinking caffeine or non-caffeine drinks. 85 volunteers drank caffeine and 80 volunteers drank non-caffeine. The results of the number items recalled by each group are shown in the box and whisker plots. Write, Pair, Share: Write down everything you know about these plots.

4.  To get financing for your business idea of opening an online customized shoe store you need to present data on the shoe sizes you will keep in your inventory. You research several shoe stores and find out the following:  The average shoe size for adult women in the US is size 9 and for men it size 10.5.  Does this give you enough information to order your inventory? What would you want to know?

5. Outcomes  Compare/Contrast measures of center and measures of dispersion.  Understand the properties of Mean Absolute Deviation  Interpret the mean absolute deviation within practical problems.  Calculate mean absolute deviation.

6. Dispersion Variability Spread Deviation Mean Absolute Deviation Standard Deviation Variance Data Set

7. Measures of Central Tendencies  Mean ( μ, x)  Median  Mode These three new measures of variability indicate how much the data differs from the mean. Measures of Dispersion  Range only uses the minimum and maximum. Extremely sensitive to outliers.  Interquartile Range (IQR) Represents the middle 50%. It is relative to the median.  Mean Absolute Deviation  Variance  Standard Deviation

8. 1 2 3 4 5 6 7 8 9 10 X X X X X X X X X Number of Family Members How much are the sizes of the families varying from the typical size or mean? How could you prove this mathematically? What is the average size of a family?

9. X X X X X X X X X Number of Family Members How much are the sizes of the families varying or deviating from the mean? What happens to the mean family size if one of the family sizes changes to 8? If this was a balanced scaled, how could we change another family size so that the 6 remains as the mean or the point of balance? 1 2 3 4 5 6 7 8 9 10

10. X X X X X X X X X Deviation = Value - Mean 4 – 6 = -2 8 – 6 = 2 7(6 – 6) = 0 All equal 0 -2+2 What is true about the deviations to the left of the mean and to right of the mean? What is the SUM of all of the deviations? 1 2 3 4 5 6 7 8 9 10

11. X X X X X X X X X Number of Family Members What is the deviation on the left side? What happens to the mean family size if one of the family sizes changes to 2? -4 +4 What family size is needed to keep a mean of 6 ? 2 – 6 10 – 6 Is this new data set more varied then the last? 1 2 3 4 5 6 7 8 9 10

12. X X X X X X X X X Deviation = Value - Mean - 4- 4+4 2 – 6 10 – 6 Deviation can be positive or negative. The sum of the deviations is always Can deviation be 0 ? 7(6-6)=0 0.0. 1 2 3 4 5 6 7 8 9 10

13. Distance = |Deviation| = |Value – Mean| Distance Absolute Deviation |Value – Mean| | 2 – 6 | | - 4 | 4 | 10 – 6 | | 4 | 4

14. X X X X X X X X X Distance vs. Deviation +4 Can distance be 0, positive, and/or negative? 7(0) Can the sum of the distances be negative, 0, and/or positive? 1 2 3 4 5 6 7 8 9 10 ValueDeviation ( x- μ ) Distance |(x- μ )| 2(2 - 6) = -4|-4|= 4 10(10 – 6) = 4|4|= 4 6(6 – 6) = 0|0| = 0

15. X X X X X X X X B. Sum of the Absolute Deviations 8 X X A. n = 2 n =8 By just looking at the graphs, does one distribution have more variability than the other? Why? 4(1) = 4 4 4 What is the typical or average deviation? 1 2 3 4 5 6 7 8 9 10 Sum of the Absolute Deviations 8 Mean of the distance =

16. X X X X X X X X X Number of Family Members Discuss with your partner what family size would be needed to keep it balanced with a mean of 6. +5 +1 +4 1 2 3 4 5 6 7 8 9 10 Calculate the mean of the absolute deviations.

17. X X X X X X X X X Number of Family Members How varied or spread out are the family sizes in comparison to the original? +4 +1 +3 1 2 3 4 5 6 7 8 9 10 Which value has the largest absolute deviation?

18. X X X X X X X X X Number of Family Members Some of the family sizes changed. One changed to 7 and the other 10. If you could change more than one family size, what could be some other configurations? With your partner, create 2 different graphs. You can’t change the 7 and 10. For each of your examples, use absolute deviation (distance) to show your mean is still 6. 1 2 3 4 5 6 7 8 9 10

19. X X X X X X X X X A. 1 2 3 4 5 6 7 8 9 10 X X X X X X X X X B. Which data is more dispersed? Why? Each data set has 9 elements or n = 9 Range = 10 – 2 = 8Range = 9 – 1 = 8 What is the range for each distribution? Why not just use range?

20. 1 2 3 4 5 6 7 8 9 10 X X X X X X X X X A. 1 2 3 4 5 6 7 8 9 10 X X X X X X X X X B. Variability -4 4 -5 -4 3(3) = 6 What is the mean absolute deviation for each? 7(0) = 0 4(0) = 0

21.  Get into groups of 2 or 3.  One person should pick up a worksheet for each partner, a piece of graph paper, and 1 stack of sticky notes.  Another team member gets a calculator for everyone in the group.

22.  For each problem  Distribute 9 sticky notes amongst the team members.  Create a distribution representing 9 family sizes that meets the requirements on the worksheet problems. Take turns placing the sticky notes.  Once created, everyone copies it on their worksheet using Xs.  Calculate the mean absolute deviation.  I will ask you to recreate one of your problems on the graph paper. Once complete, write the mean absolute deviation in the upper right hand corner.

23. Example  Symmetric  μ = 5  One family size is 2 1 2 3 4 5 6 7 8 9 10

24. Mean Absolute Deviation Average Absolute Value | | Value – Mean Average Size of the Absolute Deviations

25. Mean Absolute Deviation deviation absolute value divided by Sum (n deviations) data value mean # of data

26. Mean Absolute Deviation deviation absolute value divided by Sum (n deviations) xixi x i - μ | x i – μ| 44 - 8= -44 69 - 8= 11 1111- 8= 33 SUM 8 Data = (4,9,11) n= 3 1.Calculate μ. μ = (4+9+11) / 3 = 8 M. A. D. =

27. Which graph is more variable? Why? 1 2 3 4 5 6 7 8 9 10 X X X X X X X X X A. 1 2 3 4 5 6 7 8 9 10 X X X X X X X X X B. Each data set has 9 elements or n = 9 Partner B tell Partner A which one is more variable and why you think so. Partner A decide if you agree with Partner B. If not explain your answer. You must also be able to justified your decision by using the term “absolute deviation”.

28. X X X X X X X X B. Sum of the Absolute Deviations 8 M.A.D. = X X A. n = 2 n =8 What is the mean for each data set? By just looking at the graphs, does one distribution have more variability than the other? Why? 4(1) = 4 4 4 Determine if the Mean Absolute Deviation supports your decision. 1 2 3 4 5 6 7 8 9 10 Sum of the Absolute Deviations 8 M.A.D. =

29. To Clear Lists 1.From the home screen click on STAT. 2.Select 1:Edit a)Cursor up to highlight L1 b)CLEAR, ENTER

30. Calculate Mean Absolute Deviation of data in L1 First calculate the mean of L1 1.STAT, Calc, 1:1-Var Stats, L1 Next calculate the absolute deviations 2.From the home screen click on STAT. 3.Cursor to L2 to highlight L2 4.ENTER (“L2= “ displays at bottom) L2 = abs (L1 – x) 5.MATH, NUM, 1:abs 6.Press 2 nd 1 (to get L1) 7.-, type the mean value, ) or -, VARS, 5:Statistics, 2: x ) Now Calculate the Mean of the Absolute Deviations 8.STAT, Calc, 1:1-Var Stats, L2 9. of L2 will be the mean absolute deviation

31. To get financing for your business idea of opening an online customized shoe store you need to present data on the shoe sizes you will keep in your inventory. You research several shoe stores. 1.Using the shoe size data collected from the class determine the mean and mean absolute deviation. 2.How does knowing the mean absolute deviation of shoe sizes affect how you order your inventory? You-nique Shoes

32. To get financing for your business idea of opening an online customized shoe store you need to present data on the shoe sizes you will keep in your inventory. You researched several shoe stores and found out the following: The average shoe size for adult women in the US is size 9 and for men it size 10.5. How would knowing the mean absolute deviation in sales of shoe sizes for women affect how you order your inventory.

33. 1.Find the Mean Absolute Deviation of the data. (20, 25, 30, 30, 35,40} 2.What is the sum of the deviations of a set of data? 3.Can two sets of data have the same mean and different mean absolute deviations. Explain. 4.Can two sets of data have different means but the same mean absolute deviation.