Finite Math Examples

$7$ , $3$

Step 1

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

$\overline{x} = \frac{7 + 3}{2}$

Step 2

Add $7$ and $3$ .

$\overline{x} = \frac{10}{2}$

Step 3

Divide $10$ by $2$ .

$\overline{x} = 5$

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.

$s = \frac{{(7 - 5)}^{2} + {(3 - 5)}^{2}}{2 - 1}$

Step 6

Simplify the result.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Subtract $5$ from $7$ .

$s = \frac{2^{2} + {(3 - 5)}^{2}}{2 - 1}$

Step 6.1.2

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

$s = \frac{4 + {(3 - 5)}^{2}}{2 - 1}$

Step 6.1.3

Subtract $5$ from $3$ .

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

Step 6.1.4

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

$s = \frac{4 + 4}{2 - 1}$

Step 6.1.5

Add $4$ and $4$ .

$s = \frac{8}{2 - 1}$

Step 6.2

Simplify the expression.

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Step 6.2.1

Subtract $1$ from $2$ .

$s = \frac{8}{1}$

Step 6.2.2

Divide $8$ by $1$ .

$s = 8$

Step 7

Approximate the result.

$s^{2} \approx 8$