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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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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