The variance of the dataset {2,4,4,4,5,5,7,9} is which value?

• A. 4
• B. 2
• C. 6
• D. 1

Answer: (A)

Variance tells you how spread out the data are around the average. To find it, compute the mean, then square the difference between each value and that mean, and finally average those squared differences.

For the set 2, 4, 4, 4, 5, 5, 7, 9, the mean is (2+4+4+4+5+5+7+9)/8 = 40/8 = 5. The squared deviations from the mean are: (2−5)^2 = 9; each 4 is (4−5)^2 = 1, with three of them totaling 3; each 5 is (5−5)^2 = 0, totaling 0; (7−5)^2 = 4; (9−5)^2 = 16. Sum of squared deviations = 9 + 3 + 0 + 4 + 16 = 32. Dividing by the number of data points gives 32/8 = 4. So the variance is 4. If you treated the data as a sample, you’d divide by 7 instead, which would give about 4.57, but this problem uses the population variance.