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Probability, Statistics and Queueing

Taking the variance as the sum of the squared differences from the mean divided by the number of values, which of the following is the standard deviation of the 8 data values 2, 4, 4, 4, 5, 5, 7, 9?

  1. A2
  2. B4
  3. C5
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Answer: A. 2

The mean is (2 + 4 + 4 + 4 + 5 + 5 + 7 + 9) ÷ 8 = 40 ÷ 8 = 5. The squared differences from the mean are 9, 1, 1, 1, 0, 0, 4, 16, which sum to 32, so the variance is 32 ÷ 8 = 4. The standard deviation is the positive square root of the variance, √4 = 2.

  • A. Correct. The square root of the variance 4 gives a standard deviation of 2.
  • B. 4 is the variance, the value before taking the square root.
  • C. 5 is the mean of the data, not a measure of spread.
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