Finite Math Examples

$3 (30)$ , $5 (45)$ , $7 (70)$ , $9 (55)$ , $11 (10)$

Step 1

Multiply $3$ by $30$ .

$\overline{x} = 90, 5 (45), 7 (70), 9 (55), 11 (10)$

Step 2

Multiply $5$ by $45$ .

$\overline{x} = 90, 225, 7 (70), 9 (55), 11 (10)$

Step 3

Multiply $7$ by $70$ .

$\overline{x} = 90, 225, 490, 9 (55), 11 (10)$

Step 4

Multiply $9$ by $55$ .

$\overline{x} = 90, 225, 490, 495, 11 (10)$

Step 5

Multiply $11$ by $10$ .

$\overline{x} = 90, 225, 490, 495, 110$

Step 6

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

$\overline{x} = \frac{90 + 225 + 490 + 495 + 110}{5}$

Step 7

Cancel the common factor of $90 + 225 + 490 + 495 + 110$ and $5$ .

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Step 7.1

Factor $5$ out of $90$ .

$\overline{x} = \frac{5 \cdot 18 + 225 + 490 + 495 + 110}{5}$

Step 7.2

Factor $5$ out of $225$ .

$\overline{x} = \frac{5 \cdot 18 + 5 \cdot 45 + 490 + 495 + 110}{5}$

Step 7.3

Factor $5$ out of $5 \cdot 18 + 5 \cdot 45$ .

$\overline{x} = \frac{5 \cdot (18 + 45) + 490 + 495 + 110}{5}$

Step 7.4

Factor $5$ out of $490$ .

$\overline{x} = \frac{5 \cdot (18 + 45) + 5 \cdot 98 + 495 + 110}{5}$

Step 7.5

Factor $5$ out of $5 \cdot (18 + 45) + 5 (98)$ .

$\overline{x} = \frac{5 \cdot (18 + 45 + 98) + 495 + 110}{5}$

Step 7.6

Factor $5$ out of $495$ .

$\overline{x} = \frac{5 \cdot (18 + 45 + 98) + 5 \cdot 99 + 110}{5}$

Step 7.7

Factor $5$ out of $5 \cdot (18 + 45 + 98) + 5 (99)$ .

$\overline{x} = \frac{5 \cdot (18 + 45 + 98 + 99) + 110}{5}$

Step 7.8

Factor $5$ out of $110$ .

$\overline{x} = \frac{5 \cdot (18 + 45 + 98 + 99) + 5 \cdot 22}{5}$

Step 7.9

Factor $5$ out of $5 \cdot (18 + 45 + 98 + 99) + 5 (22)$ .

$\overline{x} = \frac{5 \cdot (18 + 45 + 98 + 99 + 22)}{5}$

Step 7.10

Cancel the common factors.

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Step 7.10.1

Factor $5$ out of $5$ .

$\overline{x} = \frac{5 \cdot (18 + 45 + 98 + 99 + 22)}{5 (1)}$

Step 7.10.2

Cancel the common factor.

$\overline{x} = \frac{5 \cdot (18 + 45 + 98 + 99 + 22)}{5 \cdot 1}$

Step 7.10.3

Rewrite the expression.

$\overline{x} = \frac{18 + 45 + 98 + 99 + 22}{1}$

Step 7.10.4

Divide $18 + 45 + 98 + 99 + 22$ by $1$ .

$\overline{x} = 18 + 45 + 98 + 99 + 22$

Step 8

Simplify by adding numbers.

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Step 8.1

Add $18$ and $45$ .

$\overline{x} = 63 + 98 + 99 + 22$

Step 8.2

Add $63$ and $98$ .

$\overline{x} = 161 + 99 + 22$

Step 8.3

Add $161$ and $99$ .

$\overline{x} = 260 + 22$

Step 8.4

Add $260$ and $22$ .

$\overline{x} = 282$

Step 9

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 10

Set up the formula for variance for this set of numbers.

$s = \frac{{(90 - 282)}^{2} + {(225 - 282)}^{2} + {(490 - 282)}^{2} + {(495 - 282)}^{2} + {(110 - 282)}^{2}}{5 - 1}$

Step 11

Simplify the result.

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Step 11.1

Simplify the numerator.

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Step 11.1.1

Subtract $282$ from $90$ .

$s = \frac{{(- 192)}^{2} + {(225 - 282)}^{2} + {(490 - 282)}^{2} + {(495 - 282)}^{2} + {(110 - 282)}^{2}}{5 - 1}$

Step 11.1.2

Raise $- 192$ to the power of $2$ .

$s = \frac{36864 + {(225 - 282)}^{2} + {(490 - 282)}^{2} + {(495 - 282)}^{2} + {(110 - 282)}^{2}}{5 - 1}$

Step 11.1.3

Subtract $282$ from $225$ .

$s = \frac{36864 + {(- 57)}^{2} + {(490 - 282)}^{2} + {(495 - 282)}^{2} + {(110 - 282)}^{2}}{5 - 1}$

Step 11.1.4

Raise $- 57$ to the power of $2$ .

$s = \frac{36864 + 3249 + {(490 - 282)}^{2} + {(495 - 282)}^{2} + {(110 - 282)}^{2}}{5 - 1}$

Step 11.1.5

Subtract $282$ from $490$ .

$s = \frac{36864 + 3249 + 208^{2} + {(495 - 282)}^{2} + {(110 - 282)}^{2}}{5 - 1}$

Step 11.1.6

Raise $208$ to the power of $2$ .

$s = \frac{36864 + 3249 + 43264 + {(495 - 282)}^{2} + {(110 - 282)}^{2}}{5 - 1}$

Step 11.1.7

Subtract $282$ from $495$ .

$s = \frac{36864 + 3249 + 43264 + 213^{2} + {(110 - 282)}^{2}}{5 - 1}$

Step 11.1.8

Raise $213$ to the power of $2$ .

$s = \frac{36864 + 3249 + 43264 + 45369 + {(110 - 282)}^{2}}{5 - 1}$

Step 11.1.9

Subtract $282$ from $110$ .

$s = \frac{36864 + 3249 + 43264 + 45369 + {(- 172)}^{2}}{5 - 1}$

Step 11.1.10

Raise $- 172$ to the power of $2$ .

$s = \frac{36864 + 3249 + 43264 + 45369 + 29584}{5 - 1}$

Step 11.1.11

Add $36864$ and $3249$ .

$s = \frac{40113 + 43264 + 45369 + 29584}{5 - 1}$

Step 11.1.12

Add $40113$ and $43264$ .

$s = \frac{83377 + 45369 + 29584}{5 - 1}$

Step 11.1.13

Add $83377$ and $45369$ .

$s = \frac{128746 + 29584}{5 - 1}$

Step 11.1.14

Add $128746$ and $29584$ .

$s = \frac{158330}{5 - 1}$

Step 11.2

Reduce the expression by cancelling the common factors.

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Step 11.2.1

Subtract $1$ from $5$ .

$s = \frac{158330}{4}$

Step 11.2.2

Cancel the common factor of $158330$ and $4$ .

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Step 11.2.2.1

Factor $2$ out of $158330$ .

$s = \frac{2 (79165)}{4}$

Step 11.2.2.2

Cancel the common factors.

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Step 11.2.2.2.1

Factor $2$ out of $4$ .

$s = \frac{2 \cdot 79165}{2 \cdot 2}$

Step 11.2.2.2.2

Cancel the common factor.

$s = \frac{2 \cdot 79165}{2 \cdot 2}$

Step 11.2.2.2.3

Rewrite the expression.

$s = \frac{79165}{2}$

Step 12

Approximate the result.

$s^{2} \approx 39582.5$