Basic Math Examples

$42$ , $- 25$

Step 1

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

$\overline{x} = \frac{42 - 25}{2}$

Step 2

Subtract $25$ from $42$ .

$\overline{x} = \frac{17}{2}$

Step 3

Divide.

$\overline{x} = 8.5$

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.

$s = \frac{{(42 - 8.5)}^{2} + {(- 25 - 8.5)}^{2}}{2 - 1}$

Step 6

Simplify the result.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Subtract $8.5$ from $42$ .

$s = \frac{{33.5}^{2} + {(- 25 - 8.5)}^{2}}{2 - 1}$

Step 6.1.2

Raise $33.5$ to the power of $2$ .

$s = \frac{1122.25 + {(- 25 - 8.5)}^{2}}{2 - 1}$

Step 6.1.3

Subtract $8.5$ from $- 25$ .

$s = \frac{1122.25 + {(- 33.5)}^{2}}{2 - 1}$

Step 6.1.4

Raise $- 33.5$ to the power of $2$ .

$s = \frac{1122.25 + 1122.25}{2 - 1}$

Step 6.1.5

Add $1122.25$ and $1122.25$ .

$s = \frac{2244.5}{2 - 1}$

Step 6.2

Simplify the expression.

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Step 6.2.1

Subtract $1$ from $2$ .

$s = \frac{2244.5}{1}$

Step 6.2.2

Divide $2244.5$ by $1$ .

$s = 2244.5$

Step 7

Approximate the result.

$s^{2} \approx 2244.5$