The prices (in dollars) of five books are 12, 18, 24, 30, and 36. Each price is multiplied by 0.5 and then 2 is subtracted. What is the variance of the new prices?
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Correct answer
A. 18
Principle or equation
If each data value x is transformed to ax + b, the variance of the new data is a^2 times the variance of the original data.
Why this answer is correct
Original prices: 12, 18, 24, 30, 36. Mean = (12+18+24+30+36)/5 = 120/5 = 24. Deviations: -12, -6, 0, 6, 12. Squared deviations: 144, 36, 0, 36, 144. Sum = 360. Variance = 360/5 = 72. New prices: 0.5x - 2. New variance = (0.5)^2 * 72 = 0.25 * 72 = 18.
Example
For data 2, 4, 6, variance is 8/3. If transformed to 3x + 1, new variance = 9 * (8/3) = 24.
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