1. MODULE 3: DESCRIPTIVE STATISTICS 2/6/2016BUS216: Probability & Statistics for Economics & Business 1

2. Descriptive Statistics Population parameter: a number calculated from all the population measurements that describes some aspect of the population Sample statistic: a number calculated using the sample measurements that describes some aspect of the sample Interval or Ratio level data Make inferences about populations Describe the variable of interest 2/6/2016 2

3. Descriptive Statistics Measures of Central Tendency Mean, Median, Mode, Percentiles Measures of Variation Range, IQR, MAD, Variance, Standard Deviation, Coefficient of Variation Measures of Shape Skewness, Box and Whisker Plot, Outliers Measures of Location Z score or Standard Score 2/6/2016 3

4. Measures of Central Tendency 2/6/2016 4

5. Measures of Central Tendency Percentiles, Deciles, Quartiles For a set of measurements arranged in increasing order, the pth percentile is a value such that p percent of the measurements fall at or below the value and (100-p) percent of the measurements fall at or above the value The first quartile Q1 is the 25th percentile The second quartile (median) is the 50th percentile The third quartile Q3 is the 75th percentile The interquartile range IQR is Q3 - Q1 Feb-16BUS216 Module 3 5

6. Percentiles 2/6/2016 6

7. Measures of Variation 2/6/2016 7 Descriptions of the spread or dispersion of a set of data.

8. Measures of Variation 2/6/2016 8

9. Measures of Variation Feb-16BUS216 Module 3 9

10. Measures of Variation Feb-16BUS216 Module 3 10

11. Measures of Variation Feb-16BUS216 Module 3 11

12. Measures of Variation Feb-16BUS216 Module 3 12

13. Measures of Shape 2/6/2016 13

14. Measures of Shape Feb-16BUS216 Module 3 14

15. Measures of Shape Feb-16BUS216 Module 3 15

16. Measures of Shape Feb-16BUS216 Module 3 16

17. Measures of Shape The “Box” in the plot …. Feb-16BUS216 Module 3 17 Hinge Median

18. Measures of Location Feb-16BUS216 Module 3 18

19. Normal Populations: Empirical Rule Empirical Rule 68% of the population measurements lie within one standard deviation of the mean 95% of the population measurements lie within two standard deviations of the mean 99.7% of the population measurements lie within three standard deviations of the mean Feb-16BUS216 Module 3 19

20. 2/6/2016 20

21. Non-Normal Populations: Chebychev’s Theorem 2/6/2016 21

22. Computer Applications Descriptive Statistics: Price Variable Mean StDev Variance CoefVar Minimum Q1 Median Q3 Price 98.03 57.96 3359.38 59.12 1.00 42.50 98.00 149.75 N for Variable Maximum Range IQR Mode Mode Skewness Price 199.00 198.00 107.25 10, 16, 38, 148 4 -0.03 The data contain at least five mode values. Only the smallest four are shown. Feb-16BUS216 Module 3 22