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Statistics 800: Quantitative Business Analysis for Decision Making

Statistics 800: Quantitative Business Analysis for Decision Making. Measures of Locations and Variability. Lecture Outline. A. Discussion of Problems From Chapter 3 B. Population and Sample C. Averages (Mean, Median, Mode) D. Box Plot ; Cumulative Distribution Curves

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Statistics 800: Quantitative Business Analysis for Decision Making

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

  2. Lecture Outline • A. Discussion of Problems From Chapter 3 • B. Population and Sample • C. Averages (Mean, Median, Mode) • D. Box Plot ; Cumulative Distribution Curves • E. Variance and Standard Deviation ; Coefficient of Variation 403.4

  3. Normal Bell Curve 403.4

  4. Bell Curves Cont’d 403.4

  5. Population and Sample • 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 403.4

  6. Notations 403.4

  7. Notations • Capital letters (X, Y, Z, etc.) denote variables • Lower case letters (x1, x2, x3, etc.) denote observations for X. • n = random sample size 403.4

  8. Averages (Mean, Median, Mode) • Mean of x1, x2, ….x300 for sample size n = 300. • T = total, • Mean = 403.4

  9. Mean (con’t) • Formula for computing weighted mean: 403.4

  10. Median & Mode • 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 • Mode • most frequently occurring number in the data set 403.4

  11. Ranks and Percentiles • Ranks expressed as percentages are called Percentiles of a data set are. 0th percentile 100th percentile 25th percentile (lower quartile) 50th Percentile 75th Percentile (upper quartile) 403.4

  12. Box Plot • Five number summary: • smallest value (0th percentile) • lower quartile (25th percentile) • median (50th percentile) • upper quartile (75th percentile) • largest value (100th percentile) • Box Plot is a graphical representation of the five number summary 403.4

  13. Two Box Plots

  14. Cumulative Distribution Curves • Plots data against their percentages • Easy to estimate any percentile value 403.4

  15. One More Cumulative Distribution Curve 403.4

  16. Standard Deviation and Coefficient of Variation • Sampling Variation or Sampling Error: Extent to which repeated samples may differ from each other. • Reliability of an estimate is measured by its sampling error • Standard deviation of a sample quantifies the extent to which its values vary from their mean 403.4

  17. Notation and Formula for Standard Deviation • s = sample standard deviation • Formula: 403.4

  18. An Empirical Rule • Nearly 67% of the population is inside the one S.D. interval around the mean: • Nearly 95% of the population is inside the two S.D. interval around the mean: • Nearly 99.7% of the population is inside the three S.D. interval around the mean: 403.4

  19. Coefficient of Variation • CV is a relative measure of variability; it is the standard deviation divided by the mean • Useful when the variation is better understood as a percentage 403.4

  20. Effects of Adding to or Re-Scaling Data 403.4

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