Multiple choice

The standard deviation of 100 observations is 10. If 5 is added to each observation and then the result is divided by 20, what will be the new standard deviation?

  1. 0.25

  2. 0.5

  3. 0.75

  4. 1.00
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Standard deviation is invariant to adding a constant. If each observation is divided by k, the new standard deviation is the old one divided by |k|. 10 / 20 = 0.5.

AI explanation

The standard deviation is independent of the addition of any constant to the observations, but it scales by the absolute value of the multiplicative constant when the data is divided or multiplied. The original standard deviation is 10, and the data is divided by 20. The new standard deviation is 10 divided by 20, which results in 0.5.

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