Review

1. Review • Frequency Distribution Table for • 8, 7, 10, 12, 9, 11, 10, 9, 12, 11, 7, 9, 7, 10, 10, 8, 12, 7, 10, 7 • Include frequency, proportion and percentage • Draw histogram, frequency polygon • Bivariate tables

2. Single variable frequency table

3. Single variable frequency table

4. Single variable frequency table

5. Single variable frequency table

6. Single variable frequency table

7. Bivariate frequency table 1. ∑X 2. ∑XY 3. ∑X ∑Y 4. ∑(Y-X) ∑Y 5. ∑Y2 6. (∑Y)2

8. Bivariate frequency table 1. ∑X 2. ∑XY 3. ∑X ∑Y 4. ∑(Y-X) ∑Y 5. ∑Y2 6. (∑Y)2

9. Bivariate frequency table 1. ∑X 2. ∑XY 3. ∑X ∑Y 4. ∑(Y-X) ∑Y 5. ∑Y2 6. (∑Y)2

10. Bivariate frequency table 1. ∑X 2. ∑XY 3. ∑X ∑Y 4. ∑(Y-X) ∑Y 5. ∑Y2 6. (∑Y)2

11. Measures of Central Tendency

12. Major Points • Mode • Median • Mean • Relative advantages and disadvantages • Review questions

13. Mode • The most common value • There may be several • Bimodal distribution has two distinct modes.

14. Median • Center value in an ordered series • Average of two center values for an even number of points • Median location • location of central value • defined as (N + 1)/2

15. Mean • What we normally call the “average” • Denoted as “xbar” • Calculated as • This will be our most common statistic

16. Relative Advantages • Mode • The most frequently obtained score • Not influenced by extreme scores • Median • Little influenced by extreme scores • Reasonable estimate of what most people mean by the center of a distribution Cont.

17. Advantages--cont. • Mean • Most common statistic • Easily manipulated algebraically • Good statistical properties

18. Disadvantages • Mode • May not represent a large proportion of the scores • Ignores extreme values completely • Median • Slightly less desirable statistical properties than mean • May not be good to ignore extreme values Cont.

19. Disadvantages--cont. • Mean • Too easily influenced by extreme scores • Requires some faith in interval properties of measurement.

20. Review Questions • List the advantages and disadvantages of each measure of central tendency. • Which measure would you use if you wanted to discuss performance on a test? • If your class contains many older students, what measure of average income is appropriate?