Finite Math Examples

$38$ , $62$

Step 1

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

$\overline{x} = \frac{38 + 62}{2}$

Step 2

Cancel the common factor of $38 + 62$ and $2$ .

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Step 2.1

Factor $2$ out of $38$ .

$\overline{x} = \frac{2 \cdot 19 + 62}{2}$

Step 2.2

Factor $2$ out of $62$ .

$\overline{x} = \frac{2 \cdot 19 + 2 \cdot 31}{2}$

Step 2.3

Factor $2$ out of $2 \cdot 19 + 2 \cdot 31$ .

$\overline{x} = \frac{2 \cdot (19 + 31)}{2}$

Step 2.4

Cancel the common factors.

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Step 2.4.1

Factor $2$ out of $2$ .

$\overline{x} = \frac{2 \cdot (19 + 31)}{2 (1)}$

Step 2.4.2

Cancel the common factor.

$\overline{x} = \frac{2 \cdot (19 + 31)}{2 \cdot 1}$

Step 2.4.3

Rewrite the expression.

$\overline{x} = \frac{19 + 31}{1}$

Step 2.4.4

Divide $19 + 31$ by $1$ .

$\overline{x} = 19 + 31$

Step 3

Add $19$ and $31$ .

$\overline{x} = 50$

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.

$s = \frac{{(38 - 50)}^{2} + {(62 - 50)}^{2}}{2 - 1}$

Step 6

Simplify the result.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Subtract $50$ from $38$ .

$s = \frac{{(- 12)}^{2} + {(62 - 50)}^{2}}{2 - 1}$

Step 6.1.2

Raise $- 12$ to the power of $2$ .

$s = \frac{144 + {(62 - 50)}^{2}}{2 - 1}$

Step 6.1.3

Subtract $50$ from $62$ .

$s = \frac{144 + 12^{2}}{2 - 1}$

Step 6.1.4

Raise $12$ to the power of $2$ .

$s = \frac{144 + 144}{2 - 1}$

Step 6.1.5

Add $144$ and $144$ .

$s = \frac{288}{2 - 1}$

Step 6.2

Simplify the expression.

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Step 6.2.1

Subtract $1$ from $2$ .

$s = \frac{288}{1}$

Step 6.2.2

Divide $288$ by $1$ .

$s = 288$

Step 7

Approximate the result.

$s^{2} \approx 288$