Finite Math Examples

0 - 49

$0 - 49$ ,

50 - 99

$50 - 99$ ,

100 - 149

$100 - 149$ ,

150 - 199

$150 - 199$ ,

200 - 249

$200 - 249$ ,

250 - 299

$250 - 299$ ,

300 - 349

$300 - 349$

Step 1

Subtract

49

$49$ from

0

$0$ .

¯ x = - 49, 50 - 99, 100 - 149, 150 - 199, 200 - 249, 250 - 299, 300 - 349

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

Step 2

Subtract

99

$99$ from

50

$50$ .

¯ x = - 49, - 49, 100 - 149, 150 - 199, 200 - 249, 250 - 299, 300 - 349

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

Step 3

Subtract

149

$149$ from

100

$100$ .

¯ x = - 49, - 49, - 49, 150 - 199, 200 - 249, 250 - 299, 300 - 349

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

Step 4

Subtract

199

$199$ from

150

$150$ .

¯ x = - 49, - 49, - 49, - 49, 200 - 249, 250 - 299, 300 - 349

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

Step 5

Subtract

249

$249$ from

200

$200$ .

¯ x = - 49, - 49, - 49, - 49, - 49, 250 - 299, 300 - 349

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

Step 6

Subtract

299

$299$ from

250

$250$ .

¯ x = - 49, - 49, - 49, - 49, - 49, - 49, 300 - 349

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

Step 7

Subtract

349

$349$ from

300

$300$ .

¯ x = - 49, - 49, - 49, - 49, - 49, - 49, - 49

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

Step 8

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

¯ x = \frac{- 49 - 49 - 49 - 49 - 49 - 49 - 49}{7}

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

Step 9

Cancel the common factor of

- 49 - 49 - 49 - 49 - 49 - 49 - 49

$- 49 - 49 - 49 - 49 - 49 - 49 - 49$ and

7

$7$ .

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Step 9.1

Factor

7

$7$ out of

- 49

$- 49$ .

¯ x = \frac{7 \cdot - 7 - 49 - 49 - 49 - 49 - 49 - 49}{7}

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

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

Raising

$0$ to any positive power yields

$0$ .

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

Step 13.1.3

Add

$- 49$ and

$49$ .

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

Step 13.1.4

Raising

$0$ to any positive power yields

$0$ .

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

Step 13.1.5

Add

$- 49$ and

$49$ .

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

Step 13.1.6

Raising

$0$ to any positive power yields

$0$ .

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

Step 13.1.7

Add

$- 49$ and

$49$ .

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

Step 13.1.8

Raising

$0$ to any positive power yields

$0$ .

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

Step 13.1.9

Add

$- 49$ and

$49$ .

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

Step 13.1.10

Raising

$0$ to any positive power yields

$0$ .

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

Step 13.1.11

Add

$- 49$ and

$49$ .

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

Step 13.1.12

Raising

$0$ to any positive power yields

$0$ .

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

Step 13.1.13

Add

$- 49$ and

$49$ .

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

Step 13.1.14

Raising

$0$ to any positive power yields

$0$ .

$s = \frac{0 + 0 + 0 + 0 + 0 + 0 + 0}{7 - 1}$

Step 13.1.15

Add

$0 + 0 + 0 + 0 + 0 + 0$ and

$0$ .

$s = \frac{0 + 0 + 0 + 0 + 0 + 0}{7 - 1}$

Step 13.1.16

Add

$0 + 0 + 0 + 0 + 0$ and

$0$ .

$s = \frac{0 + 0 + 0 + 0 + 0}{7 - 1}$

Step 13.1.17

Add

$0 + 0 + 0 + 0$ and

$0$ .

$s = \frac{0 + 0 + 0 + 0}{7 - 1}$

Step 13.1.18

Add

$0 + 0 + 0$ and

$0$ .

$s = \frac{0 + 0 + 0}{7 - 1}$

Step 13.1.19

Add

$0 + 0$ and

$0$ .

$s = \frac{0 + 0}{7 - 1}$

Step 13.1.20

Add

$0$ and

$0$ .

$s = \frac{0}{7 - 1}$

Step 13.2

Simplify the expression.

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Step 13.2.1

Subtract

$1$ from

$7$ .

$s = \frac{0}{6}$

Step 13.2.2

Divide

$0$ by

$6$ .

$s = 0$

Step 14

Approximate the result.

$s^{2} \approx 0$