Finite Math Examples

$- 5$ , $- 8$

Step 1

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

$\overline{x} = \frac{- 5 - 8}{2}$

Step 2

Subtract $8$ from $- 5$ .

$\overline{x} = \frac{- 13}{2}$

Step 3

Move the negative in front of the fraction.

$\overline{x} = - \frac{13}{2}$

Step 4

Divide.

$\overline{x} = - 6.5$

Step 5

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 6

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

$s = \frac{{(- 5 + 6.5)}^{2} + {(- 8 + 6.5)}^{2}}{2 - 1}$

Step 7

Simplify the result.

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Step 7.1

Simplify the numerator.

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Step 7.1.1

Add $- 5$ and $6.5$ .

$s = \frac{{1.5}^{2} + {(- 8 + 6.5)}^{2}}{2 - 1}$

Step 7.1.2

Raise $1.5$ to the power of $2$ .

$s = \frac{2.25 + {(- 8 + 6.5)}^{2}}{2 - 1}$

Step 7.1.3

Add $- 8$ and $6.5$ .

$s = \frac{2.25 + {(- 1.5)}^{2}}{2 - 1}$

Step 7.1.4

Raise $- 1.5$ to the power of $2$ .

$s = \frac{2.25 + 2.25}{2 - 1}$

Step 7.1.5

Add $2.25$ and $2.25$ .

$s = \frac{4.5}{2 - 1}$

Step 7.2

Simplify the expression.

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Step 7.2.1

Subtract $1$ from $2$ .

$s = \frac{4.5}{1}$

Step 7.2.2

Divide $4.5$ by $1$ .

$s = 4.5$

Step 8

Approximate the result.

$s^{2} \approx 4.5$