Find the Variance 8 , 4 , 14 , 16 , 8

$8$ , $4$ , $14$ , $16$ , $8$

The mean of a set of numbers is the sum divided by the number of terms.

$\overline{x} = \frac{8 + 4 + 14 + 16 + 8}{5}$

Simplify the numerator.

Add $8$ and $4$ .

$\overline{x} = \frac{12 + 14 + 16 + 8}{5}$

Add $12$ and $14$ .

$\overline{x} = \frac{26 + 16 + 8}{5}$

Add $26$ and $16$ .

$\overline{x} = \frac{42 + 8}{5}$

Add $42$ and $8$ .

$\overline{x} = \frac{50}{5}$

Divide $50$ by $5$ .

$\overline{x} = 10$

Set up the formula for variance. The variance of a set of values is a measure of the spread of its values.

$s^{2} = \sum_{i = 1}^{n} \frac{{(x_{i} - x_{a v g})}^{2}}{n - 1}$

Set up the formula for variance for this set of numbers.

$s = \frac{{(8 - 10)}^{2} + {(4 - 10)}^{2} + {(14 - 10)}^{2} + {(16 - 10)}^{2} + {(8 - 10)}^{2}}{5 - 1}$

Simplify the result.

Simplify the numerator.

Subtract $10$ from $8$ .

$s = \frac{{(- 2)}^{2} + {(4 - 10)}^{2} + {(14 - 10)}^{2} + {(16 - 10)}^{2} + {(8 - 10)}^{2}}{5 - 1}$

Raise $- 2$ to the power of $2$ .

$s = \frac{4 + {(4 - 10)}^{2} + {(14 - 10)}^{2} + {(16 - 10)}^{2} + {(8 - 10)}^{2}}{5 - 1}$

Subtract $10$ from $4$ .

$s = \frac{4 + {(- 6)}^{2} + {(14 - 10)}^{2} + {(16 - 10)}^{2} + {(8 - 10)}^{2}}{5 - 1}$

Raise $- 6$ to the power of $2$ .

$s = \frac{4 + 36 + {(14 - 10)}^{2} + {(16 - 10)}^{2} + {(8 - 10)}^{2}}{5 - 1}$

Subtract $10$ from $14$ .

$s = \frac{4 + 36 + 4^{2} + {(16 - 10)}^{2} + {(8 - 10)}^{2}}{5 - 1}$

Raise $4$ to the power of $2$ .

$s = \frac{4 + 36 + 16 + {(16 - 10)}^{2} + {(8 - 10)}^{2}}{5 - 1}$

Subtract $10$ from $16$ .

$s = \frac{4 + 36 + 16 + 6^{2} + {(8 - 10)}^{2}}{5 - 1}$

Raise $6$ to the power of $2$ .

$s = \frac{4 + 36 + 16 + 36 + {(8 - 10)}^{2}}{5 - 1}$

Subtract $10$ from $8$ .

$s = \frac{4 + 36 + 16 + 36 + {(- 2)}^{2}}{5 - 1}$

Raise $- 2$ to the power of $2$ .

$s = \frac{4 + 36 + 16 + 36 + 4}{5 - 1}$

Add $4$ and $36$ .

$s = \frac{40 + 16 + 36 + 4}{5 - 1}$

Add $40$ and $16$ .

$s = \frac{56 + 36 + 4}{5 - 1}$

Add $56$ and $36$ .

$s = \frac{92 + 4}{5 - 1}$

Add $92$ and $4$ .

$s = \frac{96}{5 - 1}$

Simplify the expression.

Subtract $1$ from $5$ .

$s = \frac{96}{4}$

Divide $96$ by $4$ .

$s = 24$

Approximate the result.

$s^{2} \approx 24$

Find the Variance 8 , 4 , 14 , 16 , 8

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