Multiple choice

What happens to the standard deviation if you add 10 to every observation in a data set ?

  1. It remains unchanged.

  2. It is multiplied by 10.

  3. It increases by 10.

  4. It becomes 0.
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A Correct answer
Explanation

Standard deviation measures the dispersion of data points from the mean. Adding a constant to every observation shifts the mean by that constant but does not change the spread of the data points.

AI explanation

The standard deviation is a measure of dispersion or spread from the mean, and it is unaffected by the addition or subtraction of a constant to every observation in the data set. Adding 10 to every data point simply shifts the entire distribution by 10 units without changing the relative spread of the values. Therefore, the standard deviation remains exactly the same as it was originally.

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