SAT Math · One-variable data: distributions and measures of center and spread · medium
A data set has a standard deviation of 6. If a constant value of 10 is added to every value in the data set, what is the standard…
A data set has a standard deviation of 6. If a constant value of 10 is added to every value in the data set, what is the standard deviation of the new data set?
Answer and explanation
Answer: 6
Standard deviation measures how spread out the values are around the mean. Adding the same constant to every value shifts the whole data set up by 10, including the mean, but the distances between the values and the mean do not change. So the standard deviation stays 6. A common wrong answer is 16, which comes from adding 10 to the standard deviation. Another is 60, from multiplying by 10, which would be correct only if every value were multiplied by 10 instead. Adding shifts the center; multiplying scales the spread.
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