The ages of five participants in a study are 22, 24, 26, 28, and 30. What is the variance of these ages?
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Correct answer
A. 8
Principle or equation
The variance of a sample is the average of the squared deviations from the mean. For a population, it is the mean of the squared deviations. Here, the data set is treated as a population.
Why this answer is correct
First, compute the mean: (22+24+26+28+30)/5 = 130/5 = 26. Then compute each deviation from the mean: -4, -2, 0, 2, 4. Squaring these gives 16, 4, 0, 4, 16. The sum of squared deviations is 16+4+0+4+16 = 40. Divide by the number of data points (5) to get the population variance: 40/5 = 8.
Example
For data 1, 3, 5, the mean is 3, deviations are -2, 0, 2, squares are 4, 0, 4, sum is 8, variance is 8/3 ≈ 2.67.
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