Standard deviation and variance · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Measuring spread with standard deviation

Mathematics · Data & Statistics · ages 16-17
Name ______________________   Date ____________

  1. Find the mean of 2, 4, 4, 4, 5, 5, 7, 9.

    Answer: ______________

  2. Find the population variance of 2, 4, 4, 4, 5, 5, 7, 9.

    Answer: ______________

  3. The population variance of a data set is 4. What is its population standard deviation?

    • 4
    • 16
    • 2

  4. Find the population standard deviation of 2, 2, 6, 6.

    Answer: ______________

  5. A data set has population variance 25. What is its population standard deviation?

    • 25
    • 5
    • 625
    • 12.5

  6. A data set has population variance 9. What is its population standard deviation?

    Answer: ______________

  7. Sets E = {10, 20, 30} and F = {18, 20, 22} share the mean 20. Which has the larger standard deviation?

    • Set E
    • Set F
    • They are equal
    • Cannot tell from this

  8. Find the population variance of 1, 4, 5, 6, 9.

    Answer: ______________

  9. Set P with 1, 9 and set Q with 4, 6. Ana says P has the larger standard deviation. Is Ana right?

    Circle one:   True   False

  10. Set G = {5, 5, 5, 5} and set H = {3, 5, 5, 7} both have mean 5. Kai says G has standard deviation 0. Is Kai right?

    Circle one:   True   False

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Measuring spread with standard deviation W1-mt_eNpow5tIX2-s1

  1. 5 · The values add to 40 and there are 8 of them, so the mean is 5.
  2. 4 · Squared gaps from the mean 5 add to 32, and 32 over 8 is 4.
  3. 2 · Standard deviation is the root of the variance, and root 4 is 2.
  4. 2 · The mean is 4. Every gap is 2, every squared gap is 4, so the variance is 16 / 4 = 4 and the SD is 2.
  5. 5 · Standard deviation is the square root of the variance, and the root of 25 is 5.
  6. 3 · Standard deviation is the root of variance, and root 9 is 3.
  7. Set E · E strays 10 each way from 20 while F strays only 2, so E is more spread out.
  8. 6.8 · The mean is 5. The squared gaps 16, 1, 0, 1, 16 add to 34, and 34 / 5 = 6.8.
  9. True · Both sets average 5. P's values are 4 from the mean, while Q's are 1 from it.
  10. True · Every value in G equals the mean, so every gap is 0 and the SD is 0. H has gaps of 2, so its SD is larger.
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