1. 1 Distribution Summaries Measures of central tendency Mean Median Mode Measures of spread Range Standard Deviation Interquartile Range (IQR)

2. 2 Variance Formula Definitional Formula

3. 3 Variance Formula Computational Formula

4. 4 Note

5. 5 Other central tendencies Median Mode

6. 6 Median The median is the point in the center of the distribution such that half of the cases are larger and half are smaller 34 54 72 73 96 128 200 54 72 73 96 128 200

7. 7 But, where? When there are an even number of observations, there is no middle observation. There are two middle observations The median is between the two - half way between the two 54 72 73 96 128 200 (73+96)/2 = 84.5

8. 8 What happens? If top value is raised? 54 72 73 96 128 200 54 72 73 96 128 400 Mean? Raised Median? No change

9. 9 What happens? If bottom value is lowered? 54 72 73 96 128 200 0 72 73 96 128 200 Mean? Lowered Median? No change

10. 10 Mode The mode of a distribution is the value that has the most observations. 1 2 4 9 10 10 15 18 19 32 1 2 4 9 10 15 18 19 32 Mode: 10 No mode

11. 11 Compare for cohabit length Mos| Freq. 0 | 246 1 | 25 2 | 18 3 | 6 4 | 12 5 | 7 6 | 8 7 | 17 8 | 14 9 | 16 10 | 19 11 | 21 12 | 14 13 | 9 14 | 11 15 | 16 16 | 7 17 | 5 18 | 8 19 | 11 20 | 5 21 | 10 22 | 8 23 | 10 24 | 9 25 | 9 26 | 5 27 | 1 28 | 4 29 | 3 30 | 2 31 | 5 32 | 4 33 | 2 34 | 5 35 | 2 36 | 3 37 | 4 39 | 2 40 | 1 41 | 2 43 | 1 44 | 2 45 | 1 46 | 5 47 | 2 48 | 2 50 | 2 51 | 2 56 | 1 57 | 1 62 | 4 63 | 1 66 | 2 67 | 1 71 | 2 73 | 2 74 | 1 76 | 1 79 | 1 81 | 2 97 | 2 103 | 2 ------------ Tot | 626 Mode: 0 Median: 5 Mean: 11.75

12. 12 Graphically Mode Median Mean

13. 13 Another

14. 14 Central tendency Mean: find the “average” value Median: find the “middle” value Mode : find the “most common” value

15. 15 Measures of Spread Range Variance Standard deviation Interquartile range IQR

16. 16 Quartile Median is the half-way point -- half of cases are above, half are below Quartile is the quarter point There are 3 quarter points First quartile25% below Second quartile50% below Third quartile75% below

17. 17 Consider cohabitation # Months | Cohabited | Freq. Percent Cum. ------------+----------------------------------- 0 | 246 39.30 39.30 1 | 25 3.99 43.29 2 | 18 2.88 46.17 3 | 6 0.96 47.12 4 | 12 1.92 49.04 5 | 7 1.12 50.16 6 | 8 1.28 51.44... 13 | 9 1.44 69.01 14 | 11 1.76 70.77 15 | 16 2.56 73.32 16 | 7 1.12 74.44 17 | 5 0.80 75.24 18 | 8 1.28 76.52

18. 18 Graphically 0517

19. 19 Interquartile range (IQR) Difference between the third quartile and the first quartile, Q3 - Q1 Compare with the range - the difference between the maximum and the minimum, Max - Min

20. 20 Boxplot Graph based on median and IQR Lower end of box: Q1 Upper end of box: Q3 Middle line: Q2 (median) Upper whisker: 1.5*IQR above Q3 Lower whisker: 1.5*IQR below Q1 Outliers: plotted separately

21. 21 Depression Boxplot 51016.5 IQR = 16.5 - 5 = 11.5 1.5*IQR = 17.25 Upper whisker = 16.5 + 17.25 = 33.75

22. 22 Scatterplot with boxes Depression Esteem