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 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 XfP% ∑

3 XfP% ∑

4 Single variable frequency table XfP% ∑ 20

5 Single variable frequency table XfP% ∑

6 Single variable frequency table XfP% ∑

7 Bivariate frequency table 1. ∑X 2. ∑XY 3. ∑X ∑Y 4. ∑(Y-X) ∑Y 5. ∑Y 2 6. (∑Y) 2 XYXYY-XY ∑2636

8 Bivariate frequency table 1. ∑X 2. ∑XY 3. ∑X ∑Y 4. ∑(Y-X) ∑Y 5. ∑Y 2 6. (∑Y) 2 XYXYY-XY ∑263697

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

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

Measures of Central Tendency

12 Major Points ModeMedianMean 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 Average of two center values for an even number of points Median location location of central value location of central value defined as (N + 1)/2 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 The most frequently obtained score Not influenced by extreme scores Not influenced by extreme scoresMedian Little influenced by extreme scores Little influenced by extreme scores Reasonable estimate of what most people mean by the center of a distribution Reasonable estimate of what most people mean by the center of a distribution Cont.

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

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

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