Finite Math Examples

$17$ , $13$ , $13$ , $22$ , $11$ , $20$

Step 1

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

$\overline{x} = \frac{17 + 13 + 13 + 22 + 11 + 20}{6}$

Step 2

Simplify the numerator.

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Step 2.1

Add $17$ and $13$ .

$\overline{x} = \frac{30 + 13 + 22 + 11 + 20}{6}$

Step 2.2

Add $30$ and $13$ .

$\overline{x} = \frac{43 + 22 + 11 + 20}{6}$

Step 2.3

Add $43$ and $22$ .

$\overline{x} = \frac{65 + 11 + 20}{6}$

Step 2.4

Add $65$ and $11$ .

$\overline{x} = \frac{76 + 20}{6}$

Step 2.5

Add $76$ and $20$ .

$\overline{x} = \frac{96}{6}$

Step 3

Divide $96$ by $6$ .

$\overline{x} = 16$

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.

$s = \frac{{(17 - 16)}^{2} + {(13 - 16)}^{2} + {(13 - 16)}^{2} + {(22 - 16)}^{2} + {(11 - 16)}^{2} + {(20 - 16)}^{2}}{6 - 1}$

Step 6

Simplify the result.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Subtract $16$ from $17$ .

$s = \frac{1^{2} + {(13 - 16)}^{2} + {(13 - 16)}^{2} + {(22 - 16)}^{2} + {(11 - 16)}^{2} + {(20 - 16)}^{2}}{6 - 1}$

Step 6.1.2

One to any power is one.

$s = \frac{1 + {(13 - 16)}^{2} + {(13 - 16)}^{2} + {(22 - 16)}^{2} + {(11 - 16)}^{2} + {(20 - 16)}^{2}}{6 - 1}$

Step 6.1.3

Subtract $16$ from $13$ .

$s = \frac{1 + {(- 3)}^{2} + {(13 - 16)}^{2} + {(22 - 16)}^{2} + {(11 - 16)}^{2} + {(20 - 16)}^{2}}{6 - 1}$

Step 6.1.4

Raise $- 3$ to the power of $2$ .

$s = \frac{1 + 9 + {(13 - 16)}^{2} + {(22 - 16)}^{2} + {(11 - 16)}^{2} + {(20 - 16)}^{2}}{6 - 1}$

Step 6.1.5

Subtract $16$ from $13$ .

$s = \frac{1 + 9 + {(- 3)}^{2} + {(22 - 16)}^{2} + {(11 - 16)}^{2} + {(20 - 16)}^{2}}{6 - 1}$

Step 6.1.6

Raise $- 3$ to the power of $2$ .

$s = \frac{1 + 9 + 9 + {(22 - 16)}^{2} + {(11 - 16)}^{2} + {(20 - 16)}^{2}}{6 - 1}$

Step 6.1.7

Subtract $16$ from $22$ .

$s = \frac{1 + 9 + 9 + 6^{2} + {(11 - 16)}^{2} + {(20 - 16)}^{2}}{6 - 1}$

Step 6.1.8

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

$s = \frac{1 + 9 + 9 + 36 + {(11 - 16)}^{2} + {(20 - 16)}^{2}}{6 - 1}$

Step 6.1.9

Subtract $16$ from $11$ .

$s = \frac{1 + 9 + 9 + 36 + {(- 5)}^{2} + {(20 - 16)}^{2}}{6 - 1}$

Step 6.1.10

Raise $- 5$ to the power of $2$ .

$s = \frac{1 + 9 + 9 + 36 + 25 + {(20 - 16)}^{2}}{6 - 1}$

Step 6.1.11

Subtract $16$ from $20$ .

$s = \frac{1 + 9 + 9 + 36 + 25 + 4^{2}}{6 - 1}$

Step 6.1.12

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

$s = \frac{1 + 9 + 9 + 36 + 25 + 16}{6 - 1}$

Step 6.1.13

Add $1$ and $9$ .

$s = \frac{10 + 9 + 36 + 25 + 16}{6 - 1}$

Step 6.1.14

Add $10$ and $9$ .

$s = \frac{19 + 36 + 25 + 16}{6 - 1}$

Step 6.1.15

Add $19$ and $36$ .

$s = \frac{55 + 25 + 16}{6 - 1}$

Step 6.1.16

Add $55$ and $25$ .

$s = \frac{80 + 16}{6 - 1}$

Step 6.1.17

Add $80$ and $16$ .

$s = \frac{96}{6 - 1}$

Step 6.2

Subtract $1$ from $6$ .

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

Step 7

Approximate the result.

$s^{2} \approx 19.2$