Finite Math Examples

$26$ , $6.6$

Step 1

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

$\overline{x} = \frac{26 + 6.6}{2}$

Step 2

Add $26$ and $6.6$ .

$\overline{x} = \frac{32.6}{2}$

Step 3

Divide $32.6$ by $2$ .

$\overline{x} = 16.3$

Step 4

The mean should be rounded to one more decimal place than the original data. If the original data were mixed, round to one decimal place more than the least precise.

$\overline{x} = 16.3$

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.

$s = \frac{{(26 - 16.3)}^{2} + {(6.6 - 16.3)}^{2}}{2 - 1}$

Step 7

Simplify the result.

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Step 7.1

Simplify the numerator.

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Step 7.1.1

Subtract $16.3$ from $26$ .

$s = \frac{{9.7}^{2} + {(6.6 - 16.3)}^{2}}{2 - 1}$

Step 7.1.2

Raise $9.7$ to the power of $2$ .

$s = \frac{94.09 + {(6.6 - 16.3)}^{2}}{2 - 1}$

Step 7.1.3

Subtract $16.3$ from $6.6$ .

$s = \frac{94.09 + {(- 9.7)}^{2}}{2 - 1}$

Step 7.1.4

Raise $- 9.7$ to the power of $2$ .

$s = \frac{94.09 + 94.09}{2 - 1}$

Step 7.1.5

Add $94.09$ and $94.09$ .

$s = \frac{188.18}{2 - 1}$

Step 7.2

Simplify the expression.

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Step 7.2.1

Subtract $1$ from $2$ .

$s = \frac{188.18}{1}$

Step 7.2.2

Divide $188.18$ by $1$ .

$s = 188.18$

Step 8

Approximate the result.

$s^{2} \approx 188.18$