Measures of Central Tendency

1. Measures of Central Tendency 1

2. Study note – using audio slides 1 • Advantages • Revisiting them • No attention lapses • Nothing missed, everything available for comprehensive study guide come exam times • More class time available for discussion/group work/explanation/SPSS • Disadvantage • Not real time lecture/no immediate interaction w/instructor • Can result in wanting to ask questions, but not being able to • Recommendation: • Print slides before listening, make notes and write questions down as you go • Email question/s if needed in order to make progress • Listen to the slides early in the week so that there’s plenty of time to allow for communication with the instructor 2 3 4

3. Measure of Central Tendency • What SINGLE summary statistic or parameter best describes the central location of an entire distribution? • Mode: which value occurs most (what is fashionable) • Median: the middle value in the data, once it’s ranked (the 50th percentile) • Mean: mathematical balance point; arithmetic mean; mathematical mean 1 2 3 4 General note on this early stuff

4. Mode 1 • Most frequent occurrence • What if data were • 17, 19, 20, 20, 22, 23, 23, 28 • Problem: set of numbers can be bimodal, or trimodal, depending on the scores • Not a stable measure 2 3

5. Median • Rank numbers, pick middle one • What if data were • 17, 19, 20, 23, 23, 28 • Solution: add up two middle scores, divide by 2 (=21.5) • Best measure in asymmetrical distribution (ie skewed), not sensitive to extreme scores 1 2

6. Mean • Add up the numbers and divide by the sample size (number of numbers!) • Try this one… • 5,3,2,6,9 • This is the best measure of the three – after all, it uses more information than any of the others 1 2 3

7. Characteristics of the Mean • Balance point • point around which deviations sum to zero • Deviation is difference between two numbers • For instance, if scores are 5,3,2,6,9 • Mean is 5 • Sum of deviations: 0+(-2)+(-3)+1+4 • = 0 • See? 1

8. Characteristics of the Mean • Balance point • Affected by extreme scores • Scores 7, 11, 11, 14, 17 • Mean = 12, Mode and Median = 11 • Scores 7, 11, 11, 14, 170 • Mean = 42.6, Mode & Median = 11 1

9. Characteristics of the Mean • Balance point • Affected by extreme scores • Appropriate for use with interval or ratio scales of measurement 1

10. Characteristics of the Mean • Balance point • Affected by extreme scores • Appropriate for use with interval or ratio scales of measurement • More stable than Median or Mode when multiple samples drawn from the same population • Basis for inferential stats 1

11. Guidelines to choose Measure of Central Tendency • Mean is preferred because it is the basis of inferential statistics • Median may be better for skewed data? • Distribution of wealth in the US • Mode to describe average of nominal data (Percentage - relative frequency) 1

12. Normal Distribution 1 Mode 2 Median 4 Mean Scores 3

13. Positively skewed distribution 1 2 Mode Median Mean Scores

14. Negatively skewed distribution 1 Mode Median 2 Mean Scores

15. End of file…variability next.