Find the Variance 9 , 8 , 2 , 5 , 5

$9$ , $8$ , $2$ , $5$ , $5$

Step 1

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

$\overline{x} = \frac{9 + 8 + 2 + 5 + 5}{5}$

Step 2

Simplify the numerator.

Add $9$ and $8$ .

$\overline{x} = \frac{17 + 2 + 5 + 5}{5}$

Add $17$ and $2$ .

$\overline{x} = \frac{19 + 5 + 5}{5}$

Add $19$ and $5$ .

$\overline{x} = \frac{24 + 5}{5}$

Add $24$ and $5$ .

$\overline{x} = \frac{29}{5}$

Step 3

Divide.

$\overline{x} = 5.8$

Step 4

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

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

Step 5

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

$s = \frac{{(9 - 5.8)}^{2} + {(8 - 5.8)}^{2} + {(2 - 5.8)}^{2} + {(5 - 5.8)}^{2} + {(5 - 5.8)}^{2}}{5 - 1}$

Step 6

Simplify the result.

Simplify the numerator.

Subtract $5.8$ from $9$ .

$s = \frac{{3.2}^{2} + {(8 - 5.8)}^{2} + {(2 - 5.8)}^{2} + {(5 - 5.8)}^{2} + {(5 - 5.8)}^{2}}{5 - 1}$

Raise $3.2$ to the power of $2$ .

$s = \frac{10.24 + {(8 - 5.8)}^{2} + {(2 - 5.8)}^{2} + {(5 - 5.8)}^{2} + {(5 - 5.8)}^{2}}{5 - 1}$

Subtract $5.8$ from $8$ .

$s = \frac{10.24 + {2.2}^{2} + {(2 - 5.8)}^{2} + {(5 - 5.8)}^{2} + {(5 - 5.8)}^{2}}{5 - 1}$

Raise $2.2$ to the power of $2$ .

$s = \frac{10.24 + 4.84 + {(2 - 5.8)}^{2} + {(5 - 5.8)}^{2} + {(5 - 5.8)}^{2}}{5 - 1}$

Subtract $5.8$ from $2$ .

$s = \frac{10.24 + 4.84 + {(- 3.8)}^{2} + {(5 - 5.8)}^{2} + {(5 - 5.8)}^{2}}{5 - 1}$

Raise $- 3.8$ to the power of $2$ .

$s = \frac{10.24 + 4.84 + 14.44 + {(5 - 5.8)}^{2} + {(5 - 5.8)}^{2}}{5 - 1}$

Subtract $5.8$ from $5$ .

$s = \frac{10.24 + 4.84 + 14.44 + {(- 0.8)}^{2} + {(5 - 5.8)}^{2}}{5 - 1}$

Raise $- 0.8$ to the power of $2$ .

$s = \frac{10.24 + 4.84 + 14.44 + 0.64 + {(5 - 5.8)}^{2}}{5 - 1}$

Subtract $5.8$ from $5$ .

$s = \frac{10.24 + 4.84 + 14.44 + 0.64 + {(- 0.8)}^{2}}{5 - 1}$

Raise $- 0.8$ to the power of $2$ .

$s = \frac{10.24 + 4.84 + 14.44 + 0.64 + 0.64}{5 - 1}$

Add $10.24$ and $4.84$ .

$s = \frac{15.08 + 14.44 + 0.64 + 0.64}{5 - 1}$

Add $15.08$ and $14.44$ .

$s = \frac{29.52 + 0.64 + 0.64}{5 - 1}$

Add $29.52$ and $0.64$ .

$s = \frac{30.16 + 0.64}{5 - 1}$

Add $30.16$ and $0.64$ .

$s = \frac{30.8}{5 - 1}$

Simplify the expression.

Subtract $1$ from $5$ .

$s = \frac{30.8}{4}$

Divide $30.8$ by $4$ .

$s = 7.7$

Step 7

Approximate the result.

$s^{2} \approx 7.7$

Find the Variance 9 , 8 , 2 , 5 , 5

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