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2.6 Skewness and the Mean, Median, and Mode

How a long tail pulls the mean away from the median, and reading symmetry, left skew and right skew straight off a histogram.

Introductory Business Statistics 2e, 2.6 Skewness and the Mean, Median, and Mode

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5 exercises

2.6 Exercise 1

Use the following information to answer the next three exercises: State whether the data are symmetrical, skewed to the left, or skewed to the right.

  1. 1
  2. 1
  3. 1
  4. 2
  5. 2
  6. 2
  7. 2
  8. 3
  9. 3
  10. 3
  11. 3
  12. 3
  13. 3
  14. 3
  15. 3
  16. 4
  17. 4
  18. 4
  19. 5
  20. 5

2.5

2.6 Exercise 3

Use the following information to answer the next three exercises: State whether the data are symmetrical, skewed to the left, or skewed to the right.

  1. 87
  2. 87
  3. 87
  4. 87
  5. 87
  6. 88
  7. 89
  8. 89
  9. 90
  10. 91

2.5

2.6 Exercise 5

Use the following information to answer the next three exercises: State whether the data are symmetrical, skewed to the left, or skewed to the right.

When the data are symmetrical, what is the typical relationship between the mean and median?

2.5

2.6 Exercise 17

Use the following information to answer the next three exercises: State whether the data are symmetrical, skewed to the left, or skewed to the right.

Which is the greatest, the mean, the mode, or the median of the data set?

  1. 11
  2. 11
  3. 12
  4. 12
  5. 12
  6. 12
  7. 13
  8. 15
  9. 17
  10. 22
  11. 22
  12. 22

2.5

2.6 Exercise 19

Use the following information to answer the next three exercises: State whether the data are symmetrical, skewed to the left, or skewed to the right.

Of the three measures, which tends to reflect skewing the most, the mean, the mode, or the median? Why?

2.5

Adapted from Introductory Business Statistics 2e © 2023 Rice University. Licensed under CC BY 4.0. Source: Introductory Business Statistics 2e. Imported at revision 50ec917.