1. Central Tendency

2. Variables have distributions A variable is something that changes or has different values (e.g., anger). A distribution is a collection of measures, usually across people. Distributions of numbers can be summarized with numbers (called statistics or parameters).

3. Central Tendency refers to the Middle of the Distribution

4. Middle of the Distribution Mode  Most common score Median  Top from bottom 50 percent Mean  Arithmetic mean or average (Common Statistics)

5. Mode The most frequently occurring score. Can have bimodal and multimodal distributions. Modal psychology student is female. Modal number of pubs from grad school is zero. 

6. Median Score that separates top 50% from bottom 50% Even number of scores, median is half way between two middle scores.  1 2 3 4 | 5 6 7 8 – Median is 4.5 Odd number of scores, median is the middle number  1 2 3 4 5 6 7 – Median is 4

7. Mean Sum of scores divided by the number of people. Population mean is (mu) and sample mean is (X-bar). We calculate the sample mean by: We calculate the population mean by: Raw score is X. N is number of people. Sigma (Greek symbol like big E) is summation sign. Add up scores and divide by the number of people.

8. Computation of Mean X (scores)Sum = 2+4+6 = 12 2Mean = 12 / 3 = 4 4 6

9. Deviations from the Mean Deviation defined. Deviations sum to zero. Raw scores: Deviation scores: 9 8910 789 11 0 01 -2012

10. Comparison of stats (1) Mode  Good for nominal variables  Good if you need to know most frequent observation  Quick and easy

11. Comparison of stats (2) Median  Good for “bad” (skewed) distributions  Good for distributions with arbitrary ceiling or floor  Often used with distributions of money

12. Comparison of stats (3) Mean  Used for inference as well as description; best estimator of the parameter  Based on all data in the distribution  Generally preferred except for “bad” distribution.  Most commonly used statistic for central tendency.

13. Effects of Distribution Shape

14. Review What is central tendency? Mode Median Mean

15. Computation Consider the following scores: 1, 2, 2, 3, 3, 3, 4, 5 For the above set of scores, what is N?  Cannot be determined  2  3  8

16. Computation Consider the following scores: 1, 2, 2, 3, 3, 3, 4, 5 For the above set of scores, what is the percentage (relative frequency) of 2s?  2  10  20  25

17. Computation Consider the following scores: 1, 2, 2, 3, 3, 3, 4, 5 For the above set of scores, what is the mode?  2  3  4  5

18. Discussion Questions Name a variable where it would be better to find the median than the mean. Why is it misleading to say that the average person has 1.2 brothers? Why might it be useful or helpful to say it anyway?