ACT Math · Statistics and data analysis

What is the population standard deviation of the data set 4, 8, 6, 10, 12? (Round to the nearest hundredth.)

What is the population standard deviation of the data set 4, 8, 6, 10, 12? (Round to the nearest hundredth.)

Answer and explanation

Answer: G: 2.83

First find the mean: 4+8+6+10+125=405=8\frac{4+8+6+10+12}{5}=\frac{40}{5}=8. The squared deviations from the mean are 16,0,4,4,1616, 0, 4, 4, 16, which sum to 4040 and average to 405=8\frac{40}{5}=8. The standard deviation is 8≈2.83\sqrt8\approx2.83, choice G. Choice H (8.008.00) is the variance, not its square root. Choice J (3.163.16) divides the sum of squares by 44 instead of 55, which is the sample standard deviation formula. Choice F (2.002.00) is not the result of either calculation. The ACT treats a data set given in full as the population.

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