STANDARD DEVIATION 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
STANDARD DEVIATION
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.
Solution
Sure, here are the steps to calculate the population variance:
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Calculate the mean (average) of the data set. Add all the numbers together and divide by the number of values: (11 + 3 + 5 + 18 + 1 + 4 + 7) / 7 = 49 / 7 = 7
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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
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Find 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).
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