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

2 Variance Formula Definitional Formula

3 Variance Formula Computational Formula

4 Note

5 Other central tendencies Median Mode

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

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 (73+96)/2 = 84.5

8 What happens? If top value is raised? Mean? Raised Median? No change

9 What happens? If bottom value is lowered? Mean? Lowered Median? No change

10 Mode The mode of a distribution is the value that has the most observations Mode: 10 No mode

11 Compare for cohabit length Mos| Freq. 0 | | 25 2 | 18 3 | 6 4 | 12 5 | 7 6 | 8 7 | 17 8 | 14 9 | | | | | 9 14 | | | 7 17 | 5 18 | 8 19 | | 5 21 | | 8 23 | | 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 | | Tot | 626 Mode: 0 Median: 5 Mean: 11.75

12 Graphically Mode Median Mean

13 Another

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

15 Measures of Spread Range Variance Standard deviation Interquartile range IQR

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 Consider cohabitation # Months | Cohabited | Freq. Percent Cum | | | | | | | | | | | | |

18 Graphically 0517

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 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 Depression Boxplot IQR = = *IQR = Upper whisker = = 33.75

22 Scatterplot with boxes Depression Esteem