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Statistical Problems on Mean, Variance, and Coefficient of Variation

This chapter presents a series of problems focused on statistical methods involving mean, variance, and the coefficient of variation. It covers the calculations of the mean (X̄), standard deviations (SD, S0), and their respective coefficients of variation (CV) for various datasets. Detailed explanations and step-by-step solutions are provided for Problems 4-5 through 4-26, including examples and contingency tables. The chapter emphasizes understanding data trends and analysis for practical applications in statistical measurements.

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Statistical Problems on Mean, Variance, and Coefficient of Variation

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  1. Chapter 4

  2. Problem 4-5

  3. Problem 4-10

  4. Problem 4-11

  5. Problem 4-13(a)

  6. Problem 4-13(b & c)

  7. Problem 4-19(Data) X = 154 (X - X)2 = 62.80

  8. Prob 4-19 cont’d

  9. Problem 4-19(from previous edition)

  10. Problem 4-20 (from previous edition) XD = 47 X0 = 78 SD = 10 S0 = 15 • CV = (S /X) ×(100) • CVD = (10/47) ×(100) = 21.28% • CVO = (15/78) ×(100) = 19.23%

  11. Problem 4-22 (from previous edition) • X<10 = $5.25 X>60 = $92.50 • S<10 = $1.52 S>60 = $5.28 • CV = (S /X) ×(100) • CV>60 = (5.28/92.5) × 100 = 5.71% • CV<10 = (1.52/5.25) × 100 = 28.95%

  12. Problems 4-24, 25, 36 4.24. • a. 15 • b. More labor hours are required as the number of rooms increases. 4.25. a. Both variables are nominal. • b. Contingency table • c. Yes, because 32% is more than twice 15%. 4.26. a. Opinion is ordinal and number of shares is ratio. • b. Contingency table • c. Those who own over 1000 shares.

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