The heights (in cm) of five plants are 10, 12, 14, 16, and 18. If each height is multiplied by 2 and then 5 is added, what is the variance of the new data set?
16
32
64
80
Show the answer and explanation
Correct answer
B. 32
Principle or equation
If each data value is transformed as Y = aX + b, then Var(Y) = a^2 Var(X).
Why this answer is correct
The original heights have mean 14 and variance: ((10-14)^2 + (12-14)^2 + (14-14)^2 + (16-14)^2 + (18-14)^2)/5 = (16+4+0+4+16)/5 = 40/5 = 8. With a = 2 and b = 5, new variance = 2^2 * 8 = 32.
Example
If data has variance 3 and each value is multiplied by 4, new variance is 16*3 = 48.
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