Calculate the population standard deviation for the data set 1.5, 1.2, 1.1, 1.0, 1.6.

Calculate the population standard deviation for the data set 1.5, 1.2, 1.1, 1.0, 1.6.

• A. 0.259
• B. 0.260
• C. 0.300
• D. 0.230

Answer: (A)

Population standard deviation measures how spread out all the data are around the mean, using the full data set in the denominator. First find the mean: (1.5 + 1.2 + 1.1 + 1.0 + 1.6) / 5 = 6.4 / 5 = 1.28. Next, take deviations from the mean and square them: 0.22^2 = 0.0484, (-0.08)^2 = 0.0064, (-0.18)^2 = 0.0324, (-0.28)^2 = 0.0784, 0.32^2 = 0.1024. Sum of squared deviations = 0.268. Divide by N = 5 to get the population variance: 0.268 / 5 = 0.0536. The population standard deviation is the square root of this: sqrt(0.0536) ≈ 0.2316. So, the population standard deviation is about 0.232. Among the given options, 0.230 is the closest. The value 0.259 would come from using the sample standard deviation (dividing by N−1), which is not what this question asks.

Population standard deviation measures how spread out all the data are around the mean, using the full data set in the denominator.

First find the mean: (1.5 + 1.2 + 1.1 + 1.0 + 1.6) / 5 = 6.4 / 5 = 1.28.

Next, take deviations from the mean and square them:

0.22^2 = 0.0484, (-0.08)^2 = 0.0064, (-0.18)^2 = 0.0324, (-0.28)^2 = 0.0784, 0.32^2 = 0.1024.

Sum of squared deviations = 0.268. Divide by N = 5 to get the population variance: 0.268 / 5 = 0.0536. The population standard deviation is the square root of this: sqrt(0.0536) ≈ 0.2316.

So, the population standard deviation is about 0.232. Among the given options, 0.230 is the closest. The value 0.259 would come from using the sample standard deviation (dividing by N−1), which is not what this question asks.