Finite Math Examples

$774$ , $649$ , $1210$ , $546$ , $431$ , $612$

Step 1

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

$\overline{x} = \frac{774 + 649 + 1210 + 546 + 431 + 612}{6}$

Step 2

Simplify the numerator.

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Step 2.1

Add $774$ and $649$ .

$\overline{x} = \frac{1423 + 1210 + 546 + 431 + 612}{6}$

Step 2.2

Add $1423$ and $1210$ .

$\overline{x} = \frac{2633 + 546 + 431 + 612}{6}$

Step 2.3

Add $2633$ and $546$ .

$\overline{x} = \frac{3179 + 431 + 612}{6}$

Step 2.4

Add $3179$ and $431$ .

$\overline{x} = \frac{3610 + 612}{6}$

Step 2.5

Add $3610$ and $612$ .

$\overline{x} = \frac{4222}{6}$

Step 3

Cancel the common factor of $4222$ and $6$ .

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Step 3.1

Factor $2$ out of $4222$ .

$\overline{x} = \frac{2 (2111)}{6}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $6$ .

$\overline{x} = \frac{2 \cdot 2111}{2 \cdot 3}$

Step 3.2.2

Cancel the common factor.

$\overline{x} = \frac{2 \cdot 2111}{2 \cdot 3}$

Step 3.2.3

Rewrite the expression.

$\overline{x} = \frac{2111}{3}$

Step 4

Divide.

$\overline{x} = 703.\overline{6}$

Step 5

The mean should be rounded to one more decimal place than the original data. If the original data were mixed, round to one decimal place more than the least precise.

$\overline{x} = 703.7$

Step 6

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 7

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

$s = \frac{{(774 - 703.7)}^{2} + {(649 - 703.7)}^{2} + {(1210 - 703.7)}^{2} + {(546 - 703.7)}^{2} + {(431 - 703.7)}^{2} + {(612 - 703.7)}^{2}}{6 - 1}$

Step 8

Simplify the result.

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Step 8.1

Simplify the numerator.

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Step 8.1.1

Subtract $703.7$ from $774$ .

$s = \frac{{70.3}^{2} + {(649 - 703.7)}^{2} + {(1210 - 703.7)}^{2} + {(546 - 703.7)}^{2} + {(431 - 703.7)}^{2} + {(612 - 703.7)}^{2}}{6 - 1}$

Step 8.1.2

Raise $70.3$ to the power of $2$ .

$s = \frac{4942.09 + {(649 - 703.7)}^{2} + {(1210 - 703.7)}^{2} + {(546 - 703.7)}^{2} + {(431 - 703.7)}^{2} + {(612 - 703.7)}^{2}}{6 - 1}$

Step 8.1.3

Subtract $703.7$ from $649$ .

$s = \frac{4942.09 + {(- 54.7)}^{2} + {(1210 - 703.7)}^{2} + {(546 - 703.7)}^{2} + {(431 - 703.7)}^{2} + {(612 - 703.7)}^{2}}{6 - 1}$

Step 8.1.4

Raise $- 54.7$ to the power of $2$ .

$s = \frac{4942.09 + 2992.09 + {(1210 - 703.7)}^{2} + {(546 - 703.7)}^{2} + {(431 - 703.7)}^{2} + {(612 - 703.7)}^{2}}{6 - 1}$

Step 8.1.5

Subtract $703.7$ from $1210$ .

$s = \frac{4942.09 + 2992.09 + {506.3}^{2} + {(546 - 703.7)}^{2} + {(431 - 703.7)}^{2} + {(612 - 703.7)}^{2}}{6 - 1}$

Step 8.1.6

Raise $506.3$ to the power of $2$ .

$s = \frac{4942.09 + 2992.09 + 256339.69 + {(546 - 703.7)}^{2} + {(431 - 703.7)}^{2} + {(612 - 703.7)}^{2}}{6 - 1}$

Step 8.1.7

Subtract $703.7$ from $546$ .

$s = \frac{4942.09 + 2992.09 + 256339.69 + {(- 157.7)}^{2} + {(431 - 703.7)}^{2} + {(612 - 703.7)}^{2}}{6 - 1}$

Step 8.1.8

Raise $- 157.7$ to the power of $2$ .

$s = \frac{4942.09 + 2992.09 + 256339.69 + 24869.29 + {(431 - 703.7)}^{2} + {(612 - 703.7)}^{2}}{6 - 1}$

Step 8.1.9

Subtract $703.7$ from $431$ .

$s = \frac{4942.09 + 2992.09 + 256339.69 + 24869.29 + {(- 272.7)}^{2} + {(612 - 703.7)}^{2}}{6 - 1}$

Step 8.1.10

Raise $- 272.7$ to the power of $2$ .

$s = \frac{4942.09 + 2992.09 + 256339.69 + 24869.29 + 74365.29 + {(612 - 703.7)}^{2}}{6 - 1}$

Step 8.1.11

Subtract $703.7$ from $612$ .

$s = \frac{4942.09 + 2992.09 + 256339.69 + 24869.29 + 74365.29 + {(- 91.7)}^{2}}{6 - 1}$

Step 8.1.12

Raise $- 91.7$ to the power of $2$ .

$s = \frac{4942.09 + 2992.09 + 256339.69 + 24869.29 + 74365.29 + 8408.89}{6 - 1}$

Step 8.1.13

Add $4942.09$ and $2992.09$ .

$s = \frac{7934.18 + 256339.69 + 24869.29 + 74365.29 + 8408.89}{6 - 1}$

Step 8.1.14

Add $7934.18$ and $256339.69$ .

$s = \frac{264273.87 + 24869.29 + 74365.29 + 8408.89}{6 - 1}$

Step 8.1.15

Add $264273.87$ and $24869.29$ .

$s = \frac{289143.16 + 74365.29 + 8408.89}{6 - 1}$

Step 8.1.16

Add $289143.16$ and $74365.29$ .

$s = \frac{363508.45 + 8408.89}{6 - 1}$

Step 8.1.17

Add $363508.45$ and $8408.89$ .

$s = \frac{371917.34}{6 - 1}$

Step 8.2

Simplify the expression.

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Step 8.2.1

Subtract $1$ from $6$ .

$s = \frac{371917.34}{5}$

Step 8.2.2

Divide $371917.34$ by $5$ .

$s = 74383.468$

Step 9

Approximate the result.

$s^{2} \approx 74383.468$