1. Agenda Descriptive Statistics Measures of Spread - Variability

2. Statistics Descriptive Statistics Statistics to summarize and describe the data we collected Inferential Statistics Statistics to make inferences from samples to the populations

3. Measures of Dispersion/ Spread/ Variability Indicates how cases vary or differ from each other Indicates how “central” or representative the center is Indicates how homogeneous or heterogeneous the variable is

4. Types of Measures of Dispersion Frequencies / Percentages Range / Interquartile Range Standard deviation / Variance

5. Gender Distribution: Group 1 BoyGirl (n=15) Gender Number of Kids MODE = GIRL

6. Gender Distribution: Group 2 BoyGirl (n=15) Gender Number of Kids MODE = GIRL

7. Frequency Distribution Frequency / Frequency count (f ) Percentages (%) Proportions / Relative Frequency Most common measures of dispersion for nominal and ordinal variables ONLY measures of dispersion for nominal variables

8. Frequency Distribution.9393%14 Girl.4747%7 Boy.5353%8 Girl.077%1 Boy Proportion Percentage (%) Frequency ( f ) 1 2

9. Gender Distribution: Group 2 BoyGirl (n=15) Gender Number of Kids

10. Gender Distribution: Group 3 BoyGirl (n=30) Gender Number of Kids

11. Frequency Distribution.5353%8 Girl.4747%14 Boy.5353%16 Girl.4747%7 Boy Proportion Percentage (%) Frequency ( f ) 3 2

12. Range The distance between the highest score and the lowest score (highest – lowest) Can be used with numeric ordinal and interval/ratio variables

13. Example: Age 7 89 1011 Group 1 7 89 1011 Group 2 Median=10

14. Example: Range 7 89 1011 Group 1 7 89 1011 Group 2 Range = 4 ( 7 to 11)

15. Measures of Dispersion / Spread NominalOrdinal Frequency, % Range, IQR StandardDeviatn, Variance Interval/Ratio

17. Deviation Difference from Standard In statistics, difference from the mean

18. Distribution: Age AGE (n=15) 7891011 Number of Kids Mean = 9.53 - 2.53 -1.53 * 2 - 0.53 * 40.47 * 4 1.47 * 4

19. Age: Mean - 2.53 - 1.53 * 2 - 0.53 * 4 1.47 * 4 0.47 * 4 Mean = 9.53 Sum of Negative Deviation = 7.7 Sum of Positive Deviation = 7.7

20. Variance / Standard Deviation Measures of dispersion for interval/ratio variables Variance (S 2 ): Approximate average of the squared deviations from the mean Standard Deviation(S or SD): Square root of variance The larger the variance or SD is, the higher variability the data has

21. Variance X i = Value of Each case X bar = Mean N = Sample size S 2 = N - 1 2

22. Standard Deviation S= X i = Value of Each case X bar = Mean N = Sample size 2

23. The Root-Mean-Square-Deviation or Standard Deviation Root Mean Square Deviation  n-1 ( ) X - X 2  (X – X) 2 n-1 Mean =  X n

24. Example: Age – Group 1 7891011 AGE Number of Kids (n=15) Mean = 9

25. Example: Age – Group 2 7891011 AGE Number of Kids (n=15) Mean = 9

26. Example: Age – Group 1 7891011 AGE Number of Kids (n=15) Mean = 9

27. Example: Age – Group 2 7891011 AGE Number of Kids (n=15) Mean = 9

28. Variance/Standard Deviation Group 1 Group 2

29. What are the Mean and Standard deviation for the above distribution?

30. Why is Standard Deviation an important measure of spread? Because it’s a sort of average of how much scores deviate around the mean. High SDs indicate large variation in scores, or distributions that vary widely from the mean. Because it has an important relationship with the normal distribution: THE 68-95-99.7 RULE.

31. -3s -2s -1s X +1s +2s +3s Mean +/- 1 s d covers 68% of the population Mean +/- 2 s d covers 95% of the population Mean +/- 3 s d covers 99.7% of the population The 68-95-99.7 Rule 68% 95% 99.7% 50%