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The standard deviation of the data set {1, 4, 5, 7, 8} is approximately 2.45. If every number in the data set is increased by 10, what will be the new standard deviation?

1. 2.45 nearly
2. 24.45 nearly
3. 0.245 nearly
4. 12.45 nearly

Correct answer: 2.45 nearly

Solution

Standard deviation is a measure of spread and is unaffected by adding or subtracting any constant to all data values. Shifting all values by +10 shifts the mean by 10 but keeps the deviations from the mean unchanged, so the standard deviation remains 2.45.

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