The numbers 4, 8, 12, 16, and 20 have a mean of 12 and a variance of 32. If each number is multiplied by 2, what is the variance of the new data set?
32
64
128
256
Show the answer and explanation
Correct answer
C. 128
Principle or equation
If every data point is multiplied by a constant k, the variance is multiplied by k^2.
Why this answer is correct
Original variance = 32. Multiply by 2, so new variance = 32 * 2^2 = 32 * 4 = 128.
Example
If data has variance 5 and each value is tripled, new variance = 5 * 9 = 45.
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