Finite Math Examples

$0 - 49$ , $50 - 99$ , $100 - 149$ , $150 - 199$ , $200 - 249$ , $250 - 299$ , $300 - 349$

Step 1

Subtract $49$ from $0$ .

$\overline{x} = - 49, 50 - 99, 100 - 149, 150 - 199, 200 - 249, 250 - 299, 300 - 349$

Step 2

Subtract $99$ from $50$ .

$\overline{x} = - 49, - 49, 100 - 149, 150 - 199, 200 - 249, 250 - 299, 300 - 349$

Step 3

Subtract $149$ from $100$ .

$\overline{x} = - 49, - 49, - 49, 150 - 199, 200 - 249, 250 - 299, 300 - 349$

Step 4

Subtract $199$ from $150$ .

$\overline{x} = - 49, - 49, - 49, - 49, 200 - 249, 250 - 299, 300 - 349$

Step 5

Subtract $249$ from $200$ .

$\overline{x} = - 49, - 49, - 49, - 49, - 49, 250 - 299, 300 - 349$

Step 6

Subtract $299$ from $250$ .

$\overline{x} = - 49, - 49, - 49, - 49, - 49, - 49, 300 - 349$

Step 7

Subtract $349$ from $300$ .

$\overline{x} = - 49, - 49, - 49, - 49, - 49, - 49, - 49$

Step 8

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

$\overline{x} = \frac{- 49 - 49 - 49 - 49 - 49 - 49 - 49}{7}$

Step 9

Cancel the common factor of $- 49 - 49 - 49 - 49 - 49 - 49 - 49$ and $7$ .

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Step 9.1

Factor $7$ out of $- 49$ .

$\overline{x} = \frac{7 \cdot - 7 - 49 - 49 - 49 - 49 - 49 - 49}{7}$

Step 9.2

Factor $7$ out of $- 49$ .

$\overline{x} = \frac{7 \cdot - 7 + 7 \cdot - 7 - 49 - 49 - 49 - 49 - 49}{7}$

Step 9.3

Factor $7$ out of $7 \cdot - 7 + 7 \cdot - 7$ .

$\overline{x} = \frac{7 \cdot (- 7 - 7) - 49 - 49 - 49 - 49 - 49}{7}$

Step 9.4

Factor $7$ out of $- 49$ .

$\overline{x} = \frac{7 \cdot (- 7 - 7) + 7 \cdot - 7 - 49 - 49 - 49 - 49}{7}$

Step 9.5

Factor $7$ out of $7 \cdot (- 7 - 7) + 7 (- 7)$ .

$\overline{x} = \frac{7 \cdot (- 7 - 7 - 7) - 49 - 49 - 49 - 49}{7}$

Step 9.6

Factor $7$ out of $- 49$ .

$\overline{x} = \frac{7 \cdot (- 7 - 7 - 7) + 7 \cdot - 7 - 49 - 49 - 49}{7}$

Step 9.7

Factor $7$ out of $7 \cdot (- 7 - 7 - 7) + 7 (- 7)$ .

$\overline{x} = \frac{7 \cdot (- 7 - 7 - 7 - 7) - 49 - 49 - 49}{7}$

Step 9.8

Factor $7$ out of $- 49$ .

$\overline{x} = \frac{7 \cdot (- 7 - 7 - 7 - 7) + 7 \cdot - 7 - 49 - 49}{7}$

Step 9.9

Factor $7$ out of $7 \cdot (- 7 - 7 - 7 - 7) + 7 (- 7)$ .

$\overline{x} = \frac{7 \cdot (- 7 - 7 - 7 - 7 - 7) - 49 - 49}{7}$

Step 9.10

Factor $7$ out of $- 49$ .

$\overline{x} = \frac{7 \cdot (- 7 - 7 - 7 - 7 - 7) + 7 \cdot - 7 - 49}{7}$

Step 9.11

Factor $7$ out of $7 \cdot (- 7 - 7 - 7 - 7 - 7) + 7 (- 7)$ .

$\overline{x} = \frac{7 \cdot (- 7 - 7 - 7 - 7 - 7 - 7) - 49}{7}$

Step 9.12

Factor $7$ out of $- 49$ .

$\overline{x} = \frac{7 \cdot (- 7 - 7 - 7 - 7 - 7 - 7) + 7 \cdot - 7}{7}$

Step 9.13

Factor $7$ out of $7 \cdot (- 7 - 7 - 7 - 7 - 7 - 7) + 7 (- 7)$ .

$\overline{x} = \frac{7 \cdot (- 7 - 7 - 7 - 7 - 7 - 7 - 7)}{7}$

Step 9.14

Cancel the common factors.

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Step 9.14.1

Factor $7$ out of $7$ .

$\overline{x} = \frac{7 \cdot (- 7 - 7 - 7 - 7 - 7 - 7 - 7)}{7 (1)}$

Step 9.14.2

Cancel the common factor.

$\overline{x} = \frac{7 \cdot (- 7 - 7 - 7 - 7 - 7 - 7 - 7)}{7 \cdot 1}$

Step 9.14.3

Rewrite the expression.

$\overline{x} = \frac{- 7 - 7 - 7 - 7 - 7 - 7 - 7}{1}$

Step 9.14.4

Divide $- 7 - 7 - 7 - 7 - 7 - 7 - 7$ by $1$ .

$\overline{x} = - 7 - 7 - 7 - 7 - 7 - 7 - 7$

Step 10

Simplify by subtracting numbers.

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Step 10.1

Subtract $7$ from $- 7$ .

$\overline{x} = - 14 - 7 - 7 - 7 - 7 - 7$

Step 10.2

Subtract $7$ from $- 14$ .

$\overline{x} = - 21 - 7 - 7 - 7 - 7$

Step 10.3

Subtract $7$ from $- 21$ .

$\overline{x} = - 28 - 7 - 7 - 7$

Step 10.4

Subtract $7$ from $- 28$ .

$\overline{x} = - 35 - 7 - 7$

Step 10.5

Subtract $7$ from $- 35$ .

$\overline{x} = - 42 - 7$

Step 10.6

Subtract $7$ from $- 42$ .

$\overline{x} = - 49$

Step 11

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 12

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

$s = \frac{{(- 49 + 49)}^{2} + {(- 49 + 49)}^{2} + {(- 49 + 49)}^{2} + {(- 49 + 49)}^{2} + {(- 49 + 49)}^{2} + {(- 49 + 49)}^{2} + {(- 49 + 49)}^{2}}{7 - 1}$

Step 13

Simplify the result.

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Step 13.1

Simplify the numerator.

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Step 13.1.1

Add $- 49$ and $49$ .

$s = \frac{0^{2} + {(- 49 + 49)}^{2} + {(- 49 + 49)}^{2} + {(- 49 + 49)}^{2} + {(- 49 + 49)}^{2} + {(- 49 + 49)}^{2} + {(- 49 + 49)}^{2}}{7 - 1}$

Step 13.1.2