Multiple choice

If the mean of a data set is 30 and the standard deviation is 4, what will be the new standard deviation if each observation is increased by 6?

  1. 10

  2. 4

  3. 16

  4. 24
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Standard deviation is a measure of dispersion and is invariant to change of origin (adding a constant to all observations). Therefore, it remains 4.

AI explanation

The standard deviation measures the spread of data and is unaffected by adding or subtracting a constant value from every observation. Since increasing each data point by 6 shifts the distribution without altering its spread, the standard deviation remains the same. The new standard deviation is therefore 4.

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