1. S519: Evaluation of Information Systems Social Statistics Ch3: Difference

2. Last week Social statistics Descriptive statistics Inferential statistics Mean, median and mode

3. This week Range Standard deviation Variance Using Excel to calculate them

4. The whole story Descriptive statistics Centrality tendency (average) Measurement of variability (variability) Average+Variability = describe the characteristics of a set of data

5. Measures of variability Variability How scores differ from one another Three sets of data 7, 6, 3, 3, 1 3, 4, 4, 5, 4 4, 4, 4, 4, 4 Variability = the difference from the mean

6. Measures of variability Three ways Range Standard deviation Variance

7. Range The most general measure of variability How far apart scores are from one another Range = highest score – lowest score What is the range for 98, 86, 77, 56, 48

8. Standard deviation Standard deviation (SD) Average deviation from the mean (average distance from the mean) Represents the average amount of variability

9. Exercise Calculate standard deviation 5, 8, 5, 4, 6, 7, 8, 8, 3, 6 By hand Using excel (STDEV()) Lab

10. STDEV and STDEVP STDEV is standard deviation for sample (biased SD) STDEVP is standard deviation for population (unbiased SD) If your dataset is the whole population, use STDEVP to calculate standard deviation If you dataset is the sample of something, use STDEV to calculate standard deviation

11. STDEV and STDEVP STDEV STDEVP

12. Why n or n-1? To be conservative STDEV This is the standard deviation for sample Take n-1 in order to make STDEV a bit larger than it would be. If we have err, we compensate by overestimating the STDEV

13. Why n or n-1? Sample sizeNumerator in standard deviation formula Denominator Population standard deviation STDEVP (dividing by n) Denominator Sample standard deviation STDEV (dividing by n-1) Difference between STDEVP and STDEV 105007.077.450.38 1005002.242.250.01 10005000.70710.70750.0004

14. What to remember Standard Deviation (SD) = the average distance from the mean The larger SD, the more different data are from one another Since mean is sensitive to extreme scores, so do SD If SD=0, this means that there is no variability in the set of scores (they are all identical in value) – this happens very rarely.

15. Variance Variance = (Standard Deviation)^2

16. Exercise Calculate variance in Excel 8, 8, 8, 7, 6, 6, 5, 5, 4, 3 Var()  STDEV Varp()  STDEVP Lab

17. SD vs. variance Often appears in the “Results” sections of journals They are quite different Variance is squared SD

18. SD vs. variance mean SD = 1.76 Variance = 3.1 Average distance to mean=(2+2+2+1+1 +1+2+3)/10=1.4

19. Exercise 1 (S-p78-problem2) Calculate range, STDEV and STDEVP and variance by hand or calculator 31, 42, 35, 55, 54, 34, 25, 44, 35 Use Excel to do that. Lab

20. Exercise 2 (S-p79-problem4) Problem 4 in S-p79 Calculate the variation measures for height and weight HeightWeight 53156 46131 54123 44142 56156 76171 87143 65135 45138 44114 57154 68166 65153 66140 54143 66156 51173 58143 49161 48131 Lab

21. Exercise 3 (S-p79-problem5) Western Airlines Flight Report ThursdayFridayThursdayFridayThursdayFriday Morning FlightsTo Kansas To Philadelphia To Providence Number of passengers258251303312166176 ThursdayFridayThursdayFridayThursdayFriday Evening FlightsTo Kansas To Philadelphia To Providence Number of passengers312331321331210274 Lab

22. Exercise 3 (S-p79-problem5) Look at problem 5 Write a half page summary report to your boss Form a group to discuss it Lab