The numbers 2, 4, 6, 8, and 10 have a mean of 6 and a variance of 8. If each number is multiplied by 3 and then 2 is added, what is the variance of the new data set?
24
26
72
74
Show the answer and explanation
Correct answer
C. 72
Principle or equation
If each data value is transformed by y = a x + b, then the variance of y is a^2 times the variance of x. Adding a constant does not change variance.
Why this answer is correct
Here a = 3 and b = 2. The original variance is 8. The new variance is 3^2 * 8 = 9 * 8 = 72.
Example
If original variance is 5 and each value is multiplied by 2, new variance = 4 * 5 = 20.
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