1. Measures of Central Tendency
CJ 526 Statistical Analysis in Criminal Justice

2. Introduction
Central Tendency

3. Characteristics of a Measure of Central Tendency
Single number that represents the entire set of data (average)

4. Alternate Names Also known as _____ value Average Typical Usual
Representative
Normal
Expected

5. Three Measures of Central Tendency
Mode
Median
Mean

6. The Mode
Score or qualitative category that occurs with the greatest frequency
Always used with nominal data, we find the most frequently occurring category

7. Mode Example of modal category:
Sample of 25 married, 30 single, 22 divorced
Married is the modal category
Determined by inspection, not by computation, counting up the number of times a value occurs

8. Example of Finding the Mode
Y: 1, 8, 12, 3, 8, 5, 6
Mode = 8
Can have more than one mode
1, 2, 2, 8, 10, 5, 5, 6
Mode = 2 and 5

9. The Median
The point in a distribution that divides it into two equal halves

10. Symbolized by Md

11. Finding the Median
Arrange the scores in ascending or descending numerical order

12. Finding the Median -- continued
If there is an even number of scores, the median corresponds to a value halfway between the two middle scores

13. Example of Finding the Median
Y: 1, 3, 5, 6, 8, 12
Median = 5.5

14. The Mean
The sum of the scores divided by the number of scores

15. Formula for finding the Mean
Symbolized by M or “X-bar”

16. Characteristics of the Mean
The mean may not necessarily be an actual score in a distribution

17. Deviation Score Measure of how far away a given score is from the mean
x = X - M

18. Example of Finding the Mean
Sum = 35
N = 5
M = 7

19. Selecting a Measure of Central Tendency
Choice depends on

20. Nature of the Variable
Nominal -- Mode

21. Shape of the Distribution
Symmetrical – Mean
Not symmetrical—the median will be better
Any time there are extreme scores the median will be better

22. Example
Median income: if someone loses their job, an income of 0—this would pull the average down
Median housing values: an unusually nice house or poor house would affect the average
Better to use the median

23. Intended Use of Statistic
Descriptive -- Mode, Median, or Mean

24. Central Tendency and the Shape of a Distribution
Symmetrical
Unimodal: Mo = Md = M