Finite Math Examples

$4$ , $- 20$ , $10$

Step 1

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

$\overline{x} = \frac{4 - 20 + 10}{3}$

Step 2

Simplify the numerator.

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Step 2.1

Subtract $20$ from $4$ .

$\overline{x} = \frac{- 16 + 10}{3}$

Step 2.2

Add $- 16$ and $10$ .

$\overline{x} = \frac{- 6}{3}$

Step 3

Divide $- 6$ by $3$ .

$\overline{x} = - 2$

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.

$s = \frac{{(4 + 2)}^{2} + {(- 20 + 2)}^{2} + {(10 + 2)}^{2}}{3 - 1}$

Step 6

Simplify the result.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Add $4$ and $2$ .

$s = \frac{6^{2} + {(- 20 + 2)}^{2} + {(10 + 2)}^{2}}{3 - 1}$

Step 6.1.2

Raise $6$ to the power of $2$ .

$s = \frac{36 + {(- 20 + 2)}^{2} + {(10 + 2)}^{2}}{3 - 1}$

Step 6.1.3

Add $- 20$ and $2$ .

$s = \frac{36 + {(- 18)}^{2} + {(10 + 2)}^{2}}{3 - 1}$

Step 6.1.4

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

$s = \frac{36 + 324 + {(10 + 2)}^{2}}{3 - 1}$

Step 6.1.5

Add $10$ and $2$ .

$s = \frac{36 + 324 + 12^{2}}{3 - 1}$

Step 6.1.6

Raise $12$ to the power of $2$ .

$s = \frac{36 + 324 + 144}{3 - 1}$

Step 6.1.7

Add $36$ and $324$ .

$s = \frac{360 + 144}{3 - 1}$

Step 6.1.8

Add $360$ and $144$ .

$s = \frac{504}{3 - 1}$

Step 6.2

Simplify the expression.

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Step 6.2.1

Subtract $1$ from $3$ .

$s = \frac{504}{2}$

Step 6.2.2

Divide $504$ by $2$ .

$s = 252$

Step 7

Approximate the result.

$s^{2} \approx 252$