1. Statistics 800: Quantitative Business Analysis for Decision Making Measures of Locations and Variability

2. 403.42 Lecture Outline n n A. Discussion of Problems From Chapter 3 n n B. Population and Sample n n C. Averages (Mean, Median, Mode) n n D. Box Plot ; Cumulative Distribution Curves n n E. Variance and Standard Deviation ; Coefficient of Variation

3. 403.43 Normal Bell Curve

4. 403.44 Bell Curves Cont’d

5. 403.45 Portion of the population is called sample Sample aspects are called statistics Population aspects are called parameters Population mean is denoted by µ Population standard deviation by Population and Sample

6. 403.46 Notations

7. 7 Notations n n Capital letters (X, Y, Z, etc.) denote variables n n Lower case letters (x 1, x 2, x 3, etc.) denote observations for X. n n n = random sample size

8. 403.48 Averages (Mean, Median, Mode) n n Mean of x 1, x 2, ….x 300 for sample size n = 300. n n T = total, n n Mean =

9. 403.49 Mean (con’t) n n Formula for computing weighted mean:

10. 403.410 Median & Mode n n Median – –has property that 50% of the numbers in the data set are less, and 50% are greater in magnitude – –The median need not be a number in the data set n n Mode – –most frequently occurring number in the data set

11. 403.411 Ranks and Percentiles n n Ranks expressed as percentages are called Percentiles of a data set are. 0 th percentile 100 th percentile 50th Percentile 25th percentile (lower quartile) 75th Percentile (upper quartile)

12. 403.412 Box Plot n n Five number summary: – –smallest value (0 th percentile) – –lower quartile (25 th percentile) – –median (50 th percentile) – –upper quartile (75 th percentile) – –largest value (100 th percentile) n n Box Plot is a graphical representation of the five number summary

13. Two Box Plots

14. 403.414 Cumulative Distribution Curves n n Plots data against their percentages n n Easy to estimate any percentile value

15. 403.415 One More Cumulative Distribution Curve

16. 403.416 Standard Deviation and Coefficient of Variation n n Sampling Variation or Sampling Error: Extent to which repeated samples may differ from each other. n n Reliability of an estimate is measured by its sampling error n n Standard deviation of a sample quantifies the extent to which its values vary from their mean

17. 403.417 Notation and Formula for Standard Deviation n n s = sample standard deviation n n Formula:

18. 403.418 An Empirical Rule n n Nearly 67% of the population is inside the one S.D. interval around the mean: n n Nearly 95% of the population is inside the two S.D. interval around the mean: n n Nearly 99.7% of the population is inside the three S.D. interval around the mean:

19. 403.419 Coefficient of Variation n n CV is a relative measure of variability; it is the standard deviation divided by the mean n n Useful when the variation is better understood as a percentage

20. 403.420 Effects of Adding to or Re- Scaling Data