Question
What is the Population Variance for the following numbers: 55, 37, 25, 15, 60 Level of difficulty = 1 of 2 Please format to 2 decimal places.
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Answer to a math question What is the Population Variance for the following numbers: 55, 37, 25, 15, 60 Level of difficulty = 1 of 2 Please format to 2 decimal places.
Clarabelle
4.787 Answers
1. Calculate the mean (average) of the numbers:
\bar{x} = \frac{55 + 37 + 25 + 15 + 60}{5} = \frac{192}{5} = 38.4
2. Subtract the mean and square the result for each number (i.e., \((x_i - \bar{x})^2\)):
(55 - 38.4)^2 = 16.6^2 = 275.56
(37 - 38.4)^2 = (-1.4)^2 = 1.96
(25 - 38.4)^2 = (-13.4)^2 = 179.56
(15 - 38.4)^2 = (-23.4)^2 = 547.56
(60 - 38.4)^2 = 21.6^2 = 466.56
3. Calculate the average of these squared differences to get the population variance:
\sigma^2 = \frac{275.56 + 1.96 + 179.56 + 547.56 + 466.56}{5} = \frac{1471.20}{5} = 294.24
Note: This should be rounded to 2 decimal places if needed.
Therefore, the Population Variance is
\sigma^2 = 294.24
2. Subtract the mean and square the result for each number (i.e., \((x_i - \bar{x})^2\)):
3. Calculate the average of these squared differences to get the population variance:
Note: This should be rounded to 2 decimal places if needed.
Therefore, the Population Variance is
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