Finite Math Examples

$15$ , $94$ , $84$ , $70$ , $75$ , $58$

Step 1

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

$\overline{x} = \frac{15 + 94 + 84 + 70 + 75 + 58}{6}$

Step 2

Simplify the numerator.

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Step 2.1

Add $15$ and $94$ .

$\overline{x} = \frac{109 + 84 + 70 + 75 + 58}{6}$

Step 2.2

Add $109$ and $84$ .

$\overline{x} = \frac{193 + 70 + 75 + 58}{6}$

Step 2.3

Add $193$ and $70$ .

$\overline{x} = \frac{263 + 75 + 58}{6}$

Step 2.4

Add $263$ and $75$ .

$\overline{x} = \frac{338 + 58}{6}$

Step 2.5

Add $338$ and $58$ .

$\overline{x} = \frac{396}{6}$

Step 3

Divide $396$ by $6$ .

$\overline{x} = 66$

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.

$s = \frac{{(15 - 66)}^{2} + {(94 - 66)}^{2} + {(84 - 66)}^{2} + {(70 - 66)}^{2} + {(75 - 66)}^{2} + {(58 - 66)}^{2}}{6 - 1}$

Step 6

Simplify the result.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Subtract $66$ from $15$ .

$s = \frac{{(- 51)}^{2} + {(94 - 66)}^{2} + {(84 - 66)}^{2} + {(70 - 66)}^{2} + {(75 - 66)}^{2} + {(58 - 66)}^{2}}{6 - 1}$

Step 6.1.2

Raise $- 51$ to the power of $2$ .

$s = \frac{2601 + {(94 - 66)}^{2} + {(84 - 66)}^{2} + {(70 - 66)}^{2} + {(75 - 66)}^{2} + {(58 - 66)}^{2}}{6 - 1}$

Step 6.1.3

Subtract $66$ from $94$ .

$s = \frac{2601 + 28^{2} + {(84 - 66)}^{2} + {(70 - 66)}^{2} + {(75 - 66)}^{2} + {(58 - 66)}^{2}}{6 - 1}$

Step 6.1.4

Raise $28$ to the power of $2$ .

$s = \frac{2601 + 784 + {(84 - 66)}^{2} + {(70 - 66)}^{2} + {(75 - 66)}^{2} + {(58 - 66)}^{2}}{6 - 1}$

Step 6.1.5

Subtract $66$ from $84$ .

$s = \frac{2601 + 784 + 18^{2} + {(70 - 66)}^{2} + {(75 - 66)}^{2} + {(58 - 66)}^{2}}{6 - 1}$

Step 6.1.6

Raise $18$ to the power of $2$ .

$s = \frac{2601 + 784 + 324 + {(70 - 66)}^{2} + {(75 - 66)}^{2} + {(58 - 66)}^{2}}{6 - 1}$

Step 6.1.7

Subtract $66$ from $70$ .

$s = \frac{2601 + 784 + 324 + 4^{2} + {(75 - 66)}^{2} + {(58 - 66)}^{2}}{6 - 1}$

Step 6.1.8

Raise $4$ to the power of $2$ .

$s = \frac{2601 + 784 + 324 + 16 + {(75 - 66)}^{2} + {(58 - 66)}^{2}}{6 - 1}$

Step 6.1.9

Subtract $66$ from $75$ .

$s = \frac{2601 + 784 + 324 + 16 + 9^{2} + {(58 - 66)}^{2}}{6 - 1}$

Step 6.1.10

Raise $9$ to the power of $2$ .

$s = \frac{2601 + 784 + 324 + 16 + 81 + {(58 - 66)}^{2}}{6 - 1}$

Step 6.1.11

Subtract $66$ from $58$ .

$s = \frac{2601 + 784 + 324 + 16 + 81 + {(- 8)}^{2}}{6 - 1}$

Step 6.1.12

Raise $- 8$ to the power of $2$ .

$s = \frac{2601 + 784 + 324 + 16 + 81 + 64}{6 - 1}$

Step 6.1.13

Add $2601$ and $784$ .

$s = \frac{3385 + 324 + 16 + 81 + 64}{6 - 1}$

Step 6.1.14

Add $3385$ and $324$ .

$s = \frac{3709 + 16 + 81 + 64}{6 - 1}$

Step 6.1.15

Add $3709$ and $16$ .

$s = \frac{3725 + 81 + 64}{6 - 1}$

Step 6.1.16

Add $3725$ and $81$ .

$s = \frac{3806 + 64}{6 - 1}$

Step 6.1.17

Add $3806$ and $64$ .

$s = \frac{3870}{6 - 1}$

Step 6.2

Simplify the expression.

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Step 6.2.1

Subtract $1$ from $6$ .

$s = \frac{3870}{5}$

Step 6.2.2

Divide $3870$ by $5$ .

$s = 774$

Step 7

Approximate the result.

$s^{2} \approx 774$