1. Measures of Central Tendency1

2. Study note – using audio slides1
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
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 Most frequent occurrence What if data were1
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 distribution1 2
Mode
Median
Mean
Scores

14. Negatively skewed distribution1
Mode
Median 2
Mean
Scores

15. End of file…variability next.