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Central Tendency

Central Tendency. 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).

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Central Tendency

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  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 (Common Statistics) • Mode • Most common score • Median • Top from bottom 50 percent • Mean • Arithmetic mean or average

  5. p 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

  9. Deviations from the Mean • Deviation defined. • Deviations sum to zero. • Raw scores: • Deviation scores:

  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?

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