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M ARIO F . T RIOLA

S TATISTICS. E LEMENTARY. Section 2-5 Measures of Variation . M ARIO F . T RIOLA. E IGHTH. E DITION. Jefferson Valley Bank Bank of Providence. Waiting Times of Bank Customers at Different Banks in minutes. 6.5 4.2. 6.6 5.4. 6.7 5.8. 6.8 6.2. 7.1 6.7. 7.3 7.7. 7.4 7.7.

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M ARIO F . T RIOLA

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  1. STATISTICS ELEMENTARY Section 2-5 Measures of Variation MARIO F. TRIOLA EIGHTH EDITION

  2. Jefferson Valley Bank Bank of Providence Waiting Times of Bank Customers at Different Banks in minutes 6.5 4.2 6.6 5.4 6.7 5.8 6.8 6.2 7.1 6.7 7.3 7.7 7.4 7.7 7.7 8.5 7.7 9.3 7.7 10.0 Bank of Providence Jefferson Valley Bank Mean Median Mode Midrange 7.15 7.20 7.7 7.10 7.15 7.20 7.7 7.10

  3. Waiting Times of Bank Customers at Different Banks

  4. Range lowest highest value value Measures of Variation

  5. a measure of variation of the scores about the mean (average deviation from the mean) Measures of Variation Standard Deviation

  6. Population Standard Deviation (x - µ) 2  = N Sample Standard Deviation (x - x)2 S= n -1

  7. s Sx Symbols for Standard Deviation Sample Population  x Textbook Textbook TI-83 calculators TI-83 calculators Articles in professional journals and reports often use SD for standard deviation.

  8. Carry one more decimal place than is present in the original set of values. Round only the final answer, never in the middle of a calculation. Round-off Rulefor measures of variation

  9. 0.1% The Empirical Rule (applies to bell-shaped distributions) FIGURE 2-15 99.7% of data are within 3 standard deviations of the mean 95% within 2 standard deviations 68% within 1 standard deviation 34% 34% 2.4% 2.4% 0.1% 13.5% 13.5% x - 3s x - 2s x - s x x+s x+2s x+3s

  10. minimum ‘usual’ value  (mean) - 2 (standard deviation) minimum x - 2(s) maximum ‘usual’ value  (mean) + 2 (standard deviation) maximum x + 2(s) Usual Sample Values

  11. Estimation of Standard Deviation Range Rule of Thumb x + 2s x - 2s x (maximum usual value) (minimum usual value) Range  4s or Range 4 highest value - lowest value s  = 4

  12. For typical data sets, it is unusual for a score to differ from the mean by more than 2 or 3 standard deviations. Measures of Variation Summary

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