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A data set contains the following values: 11, 3, 5, 18, 1, 4, 7. Find the population variance. Round your answer to 4 decimal places.

Question

A data set contains the following values: 11, 3, 5, 18, 1, 4, 7. Find the population variance. Round your answer to 4 decimal places.

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Solution

Sure, here are the steps to calculate the population variance:

  1. Calculate the mean (average) of the data set. Add all the numbers together and then divide by the number of values: (11 + 3 + 5 + 18 + 1 + 4 + 7) / 7 = 49 / 7 = 7

  2. Subtract the mean from each number in the data set and then square the result: (11-7)^2 = 16 (3-7)^2 = 16 (5-7)^2 = 4 (18-7)^2 = 121 (1-7)^2 = 36 (4-7)^2 = 9 (7-7)^2 = 0

  3. Calculate the mean of these squared differences: (16 + 16 + 4 + 121 + 36 + 9 + 0) / 7 = 202 / 7 = 28.8571

So, the population variance of the data set is 28.8571 (rounded to four decimal places).

This problem has been solved

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