Find the Variance 9 , 5 , 1 , 4 , 9

$9$ ,

$5$ ,

$1$ ,

$4$ ,

$9$

Step 1

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

$\overline{x} = \frac{9 + 5 + 1 + 4 + 9}{5}$

Step 2

Simplify the numerator.

Add

$9$ and

$5$ .

$\overline{x} = \frac{14 + 1 + 4 + 9}{5}$

Add

$14$ and

$1$ .

$\overline{x} = \frac{15 + 4 + 9}{5}$

Add

$15$ and

$4$ .

$\overline{x} = \frac{19 + 9}{5}$

Add

$19$ and

$9$ .

$\overline{x} = \frac{28}{5}$

Step 3

Divide.

$\overline{x} = 5.6$

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.

$s = \frac{{(9 - 5.6)}^{2} + {(5 - 5.6)}^{2} + {(1 - 5.6)}^{2} + {(4 - 5.6)}^{2} + {(9 - 5.6)}^{2}}{5 - 1}$

Step 6

Simplify the result.

Simplify the numerator.

Subtract

$5.6$ from

$9$ .

$s = \frac{{3.4}^{2} + {(5 - 5.6)}^{2} + {(1 - 5.6)}^{2} + {(4 - 5.6)}^{2} + {(9 - 5.6)}^{2}}{5 - 1}$

Raise

$3.4$ to the power of

$2$ .

$s = \frac{11.56 + {(5 - 5.6)}^{2} + {(1 - 5.6)}^{2} + {(4 - 5.6)}^{2} + {(9 - 5.6)}^{2}}{5 - 1}$

Subtract

$5.6$ from

$5$ .

$s = \frac{11.56 + {(- 0.6)}^{2} + {(1 - 5.6)}^{2} + {(4 - 5.6)}^{2} + {(9 - 5.6)}^{2}}{5 - 1}$

Raise

$- 0.6$ to the power of

$2$ .

$s = \frac{11.56 + 0.36 + {(1 - 5.6)}^{2} + {(4 - 5.6)}^{2} + {(9 - 5.6)}^{2}}{5 - 1}$

Subtract

$5.6$ from

$1$ .

$s = \frac{11.56 + 0.36 + {(- 4.6)}^{2} + {(4 - 5.6)}^{2} + {(9 - 5.6)}^{2}}{5 - 1}$

Raise

$- 4.6$ to the power of

$2$ .

$s = \frac{11.56 + 0.36 + 21.16 + {(4 - 5.6)}^{2} + {(9 - 5.6)}^{2}}{5 - 1}$

Subtract

$5.6$ from

$4$ .

$s = \frac{11.56 + 0.36 + 21.16 + {(- 1.6)}^{2} + {(9 - 5.6)}^{2}}{5 - 1}$

Raise

$- 1.6$ to the power of

$2$ .

$s = \frac{11.56 + 0.36 + 21.16 + 2.56 + {(9 - 5.6)}^{2}}{5 - 1}$

Subtract

$5.6$ from

$9$ .

$s = \frac{11.56 + 0.36 + 21.16 + 2.56 + {3.4}^{2}}{5 - 1}$

Raise

$3.4$ to the power of

$2$ .

$s = \frac{11.56 + 0.36 + 21.16 + 2.56 + 11.56}{5 - 1}$

Add

$11.56$ and

$0.36$ .

$s = \frac{11.92 + 21.16 + 2.56 + 11.56}{5 - 1}$

Add

$11.92$ and

$21.16$ .

$s = \frac{33.08 + 2.56 + 11.56}{5 - 1}$

Add

$33.08$ and

$2.56$ .

$s = \frac{35.64 + 11.56}{5 - 1}$

Add

$35.64$ and

$11.56$ .

$s = \frac{47.2}{5 - 1}$

Simplify the expression.

Subtract

$1$ from

$5$ .

$s = \frac{47.2}{4}$

Divide

$47.2$ by

$4$ .

$s = 11.8$

Step 7

Approximate the result.

$s^{2} \approx 11.8$

Find the Variance 9 , 5 , 1 , 4 , 9

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