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What is the Population Variance for the following numbers: 28, -4, 76, 68, 42 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: 28, -4, 76, 68, 42 Level of difficulty = 1 of 2 Please format to 2 decimal places

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Madelyn
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86 Answers
1. Calculate the mean \mu of the numbers:

\mu = \frac{28 + (-4) + 76 + 68 + 42}{5} = \frac{210}{5} = 42

2. Subtract the mean from each number and square the result:

(28 - 42)^2 = (-14)^2 = 196

(-4 - 42)^2 = (-46)^2 = 2116

(76 - 42)^2 = 34^2 = 1156

(68 - 42)^2 = 26^2 = 676

(42 - 42)^2 = 0^2 = 0

3. Sum the squared results:

196 + 2116 + 1156 + 676 + 0 = 4144

4. Divide by the number of data points to get the variance:

\sigma^2=\frac{4144}{5}=828.80

Answer:

828.80

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