Basic Math Examples

$- 64$ , $8$

Step 1

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

$\overline{x} = \frac{- 64 + 8}{2}$

Step 2

Cancel the common factor of $- 64 + 8$ and $2$ .

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Step 2.1

Factor $2$ out of $- 64$ .

$\overline{x} = \frac{2 \cdot - 32 + 8}{2}$

Step 2.2

Factor $2$ out of $8$ .

$\overline{x} = \frac{2 \cdot - 32 + 2 \cdot 4}{2}$

Step 2.3

Factor $2$ out of $2 \cdot - 32 + 2 \cdot 4$ .

$\overline{x} = \frac{2 \cdot (- 32 + 4)}{2}$

Step 2.4

Cancel the common factors.

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Step 2.4.1

Factor $2$ out of $2$ .

$\overline{x} = \frac{2 \cdot (- 32 + 4)}{2 (1)}$

Step 2.4.2

Cancel the common factor.

$\overline{x} = \frac{2 \cdot (- 32 + 4)}{2 \cdot 1}$

Step 2.4.3

Rewrite the expression.

$\overline{x} = \frac{- 32 + 4}{1}$

Step 2.4.4

Divide $- 32 + 4$ by $1$ .

$\overline{x} = - 32 + 4$

Step 3

Add $- 32$ and $4$ .

$\overline{x} = - 28$

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.

$s = \frac{{(- 64 + 28)}^{2} + {(8 + 28)}^{2}}{2 - 1}$

Step 6

Simplify the result.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Add $- 64$ and $28$ .

$s = \frac{{(- 36)}^{2} + {(8 + 28)}^{2}}{2 - 1}$

Step 6.1.2

Raise $- 36$ to the power of $2$ .

$s = \frac{1296 + {(8 + 28)}^{2}}{2 - 1}$

Step 6.1.3

Add $8$ and $28$ .

$s = \frac{1296 + 36^{2}}{2 - 1}$

Step 6.1.4

Raise $36$ to the power of $2$ .

$s = \frac{1296 + 1296}{2 - 1}$

Step 6.1.5

Add $1296$ and $1296$ .

$s = \frac{2592}{2 - 1}$

Step 6.2

Simplify the expression.

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Step 6.2.1

Subtract $1$ from $2$ .

$s = \frac{2592}{1}$

Step 6.2.2

Divide $2592$ by $1$ .

$s = 2592$

Step 7

Approximate the result.

$s^{2} \approx 2592$