Finite Math Examples

$57$ , $86$ , $39$ , $52$ , $30$ , $78$

Step 1

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

$\overline{x} = \frac{57 + 86 + 39 + 52 + 30 + 78}{6}$

Step 2

Simplify the numerator.

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Step 2.1

Add $57$ and $86$ .

$\overline{x} = \frac{143 + 39 + 52 + 30 + 78}{6}$

Step 2.2

Add $143$ and $39$ .

$\overline{x} = \frac{182 + 52 + 30 + 78}{6}$

Step 2.3

Add $182$ and $52$ .

$\overline{x} = \frac{234 + 30 + 78}{6}$

Step 2.4

Add $234$ and $30$ .

$\overline{x} = \frac{264 + 78}{6}$

Step 2.5

Add $264$ and $78$ .

$\overline{x} = \frac{342}{6}$

Step 3

Divide $342$ by $6$ .

$\overline{x} = 57$

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.

$s = \frac{{(57 - 57)}^{2} + {(86 - 57)}^{2} + {(39 - 57)}^{2} + {(52 - 57)}^{2} + {(30 - 57)}^{2} + {(78 - 57)}^{2}}{6 - 1}$

Step 6

Simplify the result.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Subtract $57$ from $57$ .

$s = \frac{0^{2} + {(86 - 57)}^{2} + {(39 - 57)}^{2} + {(52 - 57)}^{2} + {(30 - 57)}^{2} + {(78 - 57)}^{2}}{6 - 1}$

Step 6.1.2

Raising $0$ to any positive power yields $0$ .

$s = \frac{0 + {(86 - 57)}^{2} + {(39 - 57)}^{2} + {(52 - 57)}^{2} + {(30 - 57)}^{2} + {(78 - 57)}^{2}}{6 - 1}$

Step 6.1.3

Subtract $57$ from $86$ .

$s = \frac{0 + 29^{2} + {(39 - 57)}^{2} + {(52 - 57)}^{2} + {(30 - 57)}^{2} + {(78 - 57)}^{2}}{6 - 1}$

Step 6.1.4

Raise $29$ to the power of $2$ .

$s = \frac{0 + 841 + {(39 - 57)}^{2} + {(52 - 57)}^{2} + {(30 - 57)}^{2} + {(78 - 57)}^{2}}{6 - 1}$

Step 6.1.5

Subtract $57$ from $39$ .

$s = \frac{0 + 841 + {(- 18)}^{2} + {(52 - 57)}^{2} + {(30 - 57)}^{2} + {(78 - 57)}^{2}}{6 - 1}$

Step 6.1.6

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

$s = \frac{0 + 841 + 324 + {(52 - 57)}^{2} + {(30 - 57)}^{2} + {(78 - 57)}^{2}}{6 - 1}$

Step 6.1.7

Subtract $57$ from $52$ .

$s = \frac{0 + 841 + 324 + {(- 5)}^{2} + {(30 - 57)}^{2} + {(78 - 57)}^{2}}{6 - 1}$

Step 6.1.8

Raise $- 5$ to the power of $2$ .

$s = \frac{0 + 841 + 324 + 25 + {(30 - 57)}^{2} + {(78 - 57)}^{2}}{6 - 1}$

Step 6.1.9

Subtract $57$ from $30$ .

$s = \frac{0 + 841 + 324 + 25 + {(- 27)}^{2} + {(78 - 57)}^{2}}{6 - 1}$

Step 6.1.10

Raise $- 27$ to the power of $2$ .

$s = \frac{0 + 841 + 324 + 25 + 729 + {(78 - 57)}^{2}}{6 - 1}$

Step 6.1.11

Subtract $57$ from $78$ .

$s = \frac{0 + 841 + 324 + 25 + 729 + 21^{2}}{6 - 1}$

Step 6.1.12

Raise $21$ to the power of $2$ .

$s = \frac{0 + 841 + 324 + 25 + 729 + 441}{6 - 1}$

Step 6.1.13

Add $0$ and $841$ .

$s = \frac{841 + 324 + 25 + 729 + 441}{6 - 1}$

Step 6.1.14

Add $841$ and $324$ .

$s = \frac{1165 + 25 + 729 + 441}{6 - 1}$

Step 6.1.15

Add $1165$ and $25$ .

$s = \frac{1190 + 729 + 441}{6 - 1}$

Step 6.1.16

Add $1190$ and $729$ .

$s = \frac{1919 + 441}{6 - 1}$

Step 6.1.17

Add $1919$ and $441$ .

$s = \frac{2360}{6 - 1}$

Step 6.2

Simplify the expression.

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Step 6.2.1

Subtract $1$ from $6$ .

$s = \frac{2360}{5}$

Step 6.2.2

Divide $2360$ by $5$ .

$s = 472$

Step 7

Approximate the result.

$s^{2} \approx 472$