The weights (in kg) of five students are 50, 55, 60, 65, and 70. If each weight is multiplied by 2 and then 3 is added, what is the variance of the new data set?
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Correct answer
C. 200
Principle or equation
If each data value is transformed by y = ax + b, the variance of y is a^2 times the variance of x, because adding a constant does not affect spread.
Why this answer is correct
The original data are 50, 55, 60, 65, 70. Their mean is 60. The deviations are -10, -5, 0, 5, 10. The variance is (100 + 25 + 0 + 25 + 100) / 5 = 250 / 5 = 50. The transformation multiplies each value by 2 and adds 3, so the new variance is 2^2 * 50 = 4 * 50 = 200.
Example
For data 1, 2, 3, variance is 2/3. If each is multiplied by 3, variance becomes 9 * (2/3) = 6.
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