Finite Math Examples

$57$ , $5$ , $39$

Step 1

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

$\overline{x} = \frac{57 + 5 + 39}{3}$

Step 2

Simplify the numerator.

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Step 2.1

Add $57$ and $5$ .

$\overline{x} = \frac{62 + 39}{3}$

Step 2.2

Add $62$ and $39$ .

$\overline{x} = \frac{101}{3}$

Step 3

Divide.

$\overline{x} = 33.\overline{6}$

Step 4

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.

$\overline{x} = 33.7$

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.

$s = \frac{{(57 - 33.7)}^{2} + {(5 - 33.7)}^{2} + {(39 - 33.7)}^{2}}{3 - 1}$

Step 7

Simplify the result.

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Step 7.1

Simplify the numerator.

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Step 7.1.1

Subtract $33.7$ from $57$ .

$s = \frac{{23.3}^{2} + {(5 - 33.7)}^{2} + {(39 - 33.7)}^{2}}{3 - 1}$

Step 7.1.2

Raise $23.3$ to the power of $2$ .

$s = \frac{542.89 + {(5 - 33.7)}^{2} + {(39 - 33.7)}^{2}}{3 - 1}$

Step 7.1.3

Subtract $33.7$ from $5$ .

$s = \frac{542.89 + {(- 28.7)}^{2} + {(39 - 33.7)}^{2}}{3 - 1}$

Step 7.1.4

Raise $- 28.7$ to the power of $2$ .

$s = \frac{542.89 + 823.69 + {(39 - 33.7)}^{2}}{3 - 1}$

Step 7.1.5

Subtract $33.7$ from $39$ .

$s = \frac{542.89 + 823.69 + {5.3}^{2}}{3 - 1}$

Step 7.1.6

Raise $5.3$ to the power of $2$ .

$s = \frac{542.89 + 823.69 + 28.09}{3 - 1}$

Step 7.1.7

Add $542.89$ and $823.69$ .

$s = \frac{1366.58 + 28.09}{3 - 1}$

Step 7.1.8

Add $1366.58$ and $28.09$ .

$s = \frac{1394.67}{3 - 1}$

Step 7.2

Simplify the expression.

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Step 7.2.1

Subtract $1$ from $3$ .

$s = \frac{1394.67}{2}$

Step 7.2.2

Divide $1394.67$ by $2$ .

$s = 697.335$

Step 8

Approximate the result.

$s^{2} \approx 697.335$