Multiple choice

The standard deviation of$15$ terms is $6$ and each item is decreased by $1$. Then the standard deviation of new data is?

  1. $5$
  2. $7$
  3. $\dfrac{91}{15}$
  4. $6$
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D Correct answer
Explanation

Standard deviation is a measure of dispersion and is invariant to changes in origin (adding or subtracting a constant from every term). Thus, the standard deviation remains 6.

AI explanation

Use the property of standard deviation which states that adding or subtracting a constant from each observation does not change the standard deviation. Since every term in the data set is decreased by 1, the spread or dispersion of the data remains exactly the same. Therefore, the standard deviation of the new data remains 6.

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