Multiple choice

For a data set, mean = 40 and standard deviation = 5. If 10 is subtracted from each observation, the new standard deviation will be:

  1. 15

  2. 10

  3. 5

  4. 0
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C Correct answer
Explanation

Standard deviation is a measure of dispersion. Subtracting a constant from every observation shifts the data but does not change the spread, so the standard deviation remains the same.

AI explanation

A key property of standard deviation is that it is invariant under the addition or subtraction of a constant to every observation. Because subtracting 10 from each data point only shifts the distribution without changing its spread, the standard deviation remains unchanged. Therefore, the new standard deviation is 5.

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