Finite Math Examples

$3$ , $8$ , $13$ , $18$

Step 1

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

$\overline{x} = \frac{3 + 8 + 13 + 18}{4}$

Step 2

Simplify the numerator.

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Step 2.1

Add $3$ and $8$ .

$\overline{x} = \frac{11 + 13 + 18}{4}$

Step 2.2

Add $11$ and $13$ .

$\overline{x} = \frac{24 + 18}{4}$

Step 2.3

Add $24$ and $18$ .

$\overline{x} = \frac{42}{4}$

Step 3

Cancel the common factor of $42$ and $4$ .

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Step 3.1

Factor $2$ out of $42$ .

$\overline{x} = \frac{2 (21)}{4}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $4$ .

$\overline{x} = \frac{2 \cdot 21}{2 \cdot 2}$

Step 3.2.2

Cancel the common factor.

$\overline{x} = \frac{2 \cdot 21}{2 \cdot 2}$

Step 3.2.3

Rewrite the expression.

$\overline{x} = \frac{21}{2}$

Step 4

Divide.

$\overline{x} = 10.5$

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.

$s = \frac{{(3 - 10.5)}^{2} + {(8 - 10.5)}^{2} + {(13 - 10.5)}^{2} + {(18 - 10.5)}^{2}}{4 - 1}$

Step 7

Simplify the result.

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Step 7.1

Simplify the numerator.

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Step 7.1.1

Subtract $10.5$ from $3$ .

$s = \frac{{(- 7.5)}^{2} + {(8 - 10.5)}^{2} + {(13 - 10.5)}^{2} + {(18 - 10.5)}^{2}}{4 - 1}$

Step 7.1.2

Raise $- 7.5$ to the power of $2$ .

$s = \frac{56.25 + {(8 - 10.5)}^{2} + {(13 - 10.5)}^{2} + {(18 - 10.5)}^{2}}{4 - 1}$

Step 7.1.3

Subtract $10.5$ from $8$ .

$s = \frac{56.25 + {(- 2.5)}^{2} + {(13 - 10.5)}^{2} + {(18 - 10.5)}^{2}}{4 - 1}$

Step 7.1.4

Raise $- 2.5$ to the power of $2$ .

$s = \frac{56.25 + 6.25 + {(13 - 10.5)}^{2} + {(18 - 10.5)}^{2}}{4 - 1}$

Step 7.1.5

Subtract $10.5$ from $13$ .

$s = \frac{56.25 + 6.25 + {2.5}^{2} + {(18 - 10.5)}^{2}}{4 - 1}$

Step 7.1.6

Raise $2.5$ to the power of $2$ .

$s = \frac{56.25 + 6.25 + 6.25 + {(18 - 10.5)}^{2}}{4 - 1}$

Step 7.1.7

Subtract $10.5$ from $18$ .

$s = \frac{56.25 + 6.25 + 6.25 + {7.5}^{2}}{4 - 1}$

Step 7.1.8

Raise $7.5$ to the power of $2$ .

$s = \frac{56.25 + 6.25 + 6.25 + 56.25}{4 - 1}$

Step 7.1.9

Add $56.25$ and $6.25$ .

$s = \frac{62.5 + 6.25 + 56.25}{4 - 1}$

Step 7.1.10

Add $62.5$ and $6.25$ .

$s = \frac{68.75 + 56.25}{4 - 1}$

Step 7.1.11

Add $68.75$ and $56.25$ .

$s = \frac{125}{4 - 1}$

Step 7.2

Reduce the expression by cancelling the common factors.

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Step 7.2.1

Subtract $1$ from $4$ .

$s = \frac{125}{3}$

Step 7.2.2

Cancel the common factor of $125$ and $3$ .

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Step 7.2.2.1

Rewrite $125$ as $1 (125)$ .

$s = \frac{1 (125)}{3}$

Step 7.2.2.2

Cancel the common factors.

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Step 7.2.2.2.1

Rewrite $3$ as $1 (3)$ .

$s = \frac{1 \cdot 125}{1 \cdot 3}$

Step 7.2.2.2.2

Cancel the common factor.

$s = \frac{1 \cdot 125}{1 \cdot 3}$

Step 7.2.2.2.3

Rewrite the expression.

$s = \frac{125}{3}$

Step 8

Approximate the result.

$s^{2} \approx 41.6667$