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Measures of Dispersion for Numerical Data Practice Questions

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Updated on Oct 5, 2011

To review these concepts, go to Measures of Dispersion for Numerical Data Study Guide.

Measures of Dispersion for Numerical Data Practice Questions

Practice

  1. Find the range of the ages of the men who won the Oscar for best actor from 1996 to 2004. Their ages at the time of winning the award were 45, 59, 45, 42, 35, 46, 28, 42, and 36.
  2. Find the range of the ages of the women who won the Oscar for best actress from 1996 to 2004. Their ages at the time of receiving the award were 39, 33, 25, 24, 32, 32, 34, 27, and 30.
  3. Find the interquartile range of the ages of the men who won the Oscar for best actor from 1996 to 2004. Their ages at the time of winning the award were 45, 59, 45, 42, 35, 46, 28, 42, and 36.
  4. Find the interquartile range of the ages of the women who won the Oscar for best actress from 1996 to 2004. Their ages at the time of receiving the award were 39, 33, 25, 24, 32, 32, 34, 27, and 30.
  5. Find the mean absolute deviation of the ages of the men winning the Oscar for best actor from 1996 to 2004. Their ages at the time of winning the award were 45, 59, 45, 42, 35, 46, 28, 42, and 36.
  6. Find the mean absolute deviation of the ages of the women winning the Oscar for best actress from 1996 to 2004. Their ages at the time of receiving the award were 39, 33, 25, 24, 32, 32, 34, 27, and 30.
  7. Find the variance and standard deviation of the men who won the Oscar for best actor from 1996 to 2004. Their ages at the time of winning the award were 45, 59, 45, 42, 35, 46, 28, 42, and 36.
  8. Find the variance and standard deviation of the women who won the Oscar for best actress from 1996 to 2004. Their ages at the time of receiving the award were 39, 33, 25, 24, 32, 32, 34, 27, and 30.
  9. Compare the range, interquartile range, mean absolute deviation, and standard deviation of the population of ages of men who won the Oscar for best actor from 1996 to 2004.Which measure do you prefer? Explain.
  10. Compare the range, interquartile range, mean absolute deviation, and standard deviation of the population of ages of women who won the Oscar for best actor from 1996 to 2004.Which measure do you prefer? Explain.

Previously, we created a dotplot and a stem-and-leaf plot for the average hours of sleep for 20 high school students who had been randomly selected from a very large high school. They kept a record of the number of hours they slept each night for a week. These seven values were averaged to obtain an average night of sleep for each. The parameters that provide measures of central tendency were estimated. The 20 students slept an average of 9, 8, 8, 7.5, 6, 6, 4, 5.5, 7, 8, 5, 7.5, 6.5, 10, 8.5, 6.5, 5, 5.5, 7, and 7.5 hours.

  1. Find the sample range.
  2. Find the sample interquartile range.
  3. Find the sample mean absolute deviation.
  4. Find the sample variance and standard deviation.
  5. Which of the measures of dispersion do you think is most appropriate for these data? Explain.

Solutions

  1. 31
  2. 15
  3. 10
  4. 7.5
  5. 6.5
  6. 3.7
  7. Variance = 71.4; standard deviation = 8.4
  8. Variance = 20.0; standard deviation = 4.5.
  9. The range, mean absolute deviation, and standard deviation are not good measures because they are affected by outliers. The only measure not influenced by outliers is the interquartile range, which would be the best measure to use.
  10. Outliers affect the range, mean absolute deviation, and standard deviation, so the interquartile range would be the best measure because it is the only one not affected by outliers.
  11. 6
  12. 2.25
  13. 1.2
  14. Sample variance = 2.25; sample standard deviation = 1.5.
  15. The range, mean absolute deviation, and standard deviation are affected by outliers, so the interquartile range would be the best measure of dispersion. It is the only one not affected by outliers.
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