The heights (in cm) of five students are 150, 160, 170, 180, and 190. If each height is increased by 5 cm, what is the variance of the new data set?
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Correct answer
A. 200
Principle or equation
Adding a constant to all data values shifts the mean but does not change the variance. Variance is the average squared deviation from the mean.
Why this answer is correct
Original mean = (150+160+170+180+190)/5 = 170. Deviations: -20, -10, 0, 10, 20. Squared deviations: 400, 100, 0, 100, 400. Sum = 1000. Variance = 1000/5 = 200. Adding 5 to each value shifts the mean to 175 but deviations remain the same, so variance remains 200.
Example
Data {1,2,3} has mean 2 and variance (1+0+1)/3 = 2/3. Adding 10 gives {11,12,13}, mean 12, variance still 2/3.
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