Finite Math Examples

$4.85$ , $5.1$ , $5.5$ , $4.75$ , $4.5$ , $5$ , $6$

Step 1

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

$\overline{x} = \frac{4.85 + 5.1 + 5.5 + 4.75 + 4.5 + 5 + 6}{7}$

Step 2

Simplify the numerator.

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Step 2.1

Add $4.85$ and $5.1$ .

$\overline{x} = \frac{9.95 + 5.5 + 4.75 + 4.5 + 5 + 6}{7}$

Step 2.2

Add $9.95$ and $5.5$ .

$\overline{x} = \frac{15.45 + 4.75 + 4.5 + 5 + 6}{7}$

Step 2.3

Add $15.45$ and $4.75$ .

$\overline{x} = \frac{20.2 + 4.5 + 5 + 6}{7}$

Step 2.4

Add $20.2$ and $4.5$ .

$\overline{x} = \frac{24.7 + 5 + 6}{7}$

Step 2.5

Add $24.7$ and $5$ .

$\overline{x} = \frac{29.7 + 6}{7}$

Step 2.6

Add $29.7$ and $6$ .

$\overline{x} = \frac{35.7}{7}$

Step 3

Divide $35.7$ by $7$ .

$\overline{x} = 5.1$

Step 4

Divide.

$\overline{x} = 5.1$

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.

$s = \frac{{(4.85 - 5.1)}^{2} + {(5.1 - 5.1)}^{2} + {(5.5 - 5.1)}^{2} + {(4.75 - 5.1)}^{2} + {(4.5 - 5.1)}^{2} + {(5 - 5.1)}^{2} + {(6 - 5.1)}^{2}}{7 - 1}$

Step 7

Simplify the result.

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Step 7.1

Simplify the numerator.

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Step 7.1.1

Subtract $5.1$ from $4.85$ .

$s = \frac{{(- 0.25)}^{2} + {(5.1 - 5.1)}^{2} + {(5.5 - 5.1)}^{2} + {(4.75 - 5.1)}^{2} + {(4.5 - 5.1)}^{2} + {(5 - 5.1)}^{2} + {(6 - 5.1)}^{2}}{7 - 1}$

Step 7.1.2

Raise $- 0.25$ to the power of $2$ .

$s = \frac{0.0625 + {(5.1 - 5.1)}^{2} + {(5.5 - 5.1)}^{2} + {(4.75 - 5.1)}^{2} + {(4.5 - 5.1)}^{2} + {(5 - 5.1)}^{2} + {(6 - 5.1)}^{2}}{7 - 1}$

Step 7.1.3

Subtract $5.1$ from $5.1$ .

$s = \frac{0.0625 + 0^{2} + {(5.5 - 5.1)}^{2} + {(4.75 - 5.1)}^{2} + {(4.5 - 5.1)}^{2} + {(5 - 5.1)}^{2} + {(6 - 5.1)}^{2}}{7 - 1}$

Step 7.1.4

Raising $0$ to any positive power yields $0$ .

$s = \frac{0.0625 + 0 + {(5.5 - 5.1)}^{2} + {(4.75 - 5.1)}^{2} + {(4.5 - 5.1)}^{2} + {(5 - 5.1)}^{2} + {(6 - 5.1)}^{2}}{7 - 1}$

Step 7.1.5

Subtract $5.1$ from $5.5$ .

$s = \frac{0.0625 + 0 + {0.4}^{2} + {(4.75 - 5.1)}^{2} + {(4.5 - 5.1)}^{2} + {(5 - 5.1)}^{2} + {(6 - 5.1)}^{2}}{7 - 1}$

Step 7.1.6

Raise $0.4$ to the power of $2$ .

$s = \frac{0.0625 + 0 + 0.16 + {(4.75 - 5.1)}^{2} + {(4.5 - 5.1)}^{2} + {(5 - 5.1)}^{2} + {(6 - 5.1)}^{2}}{7 - 1}$

Step 7.1.7

Subtract $5.1$ from $4.75$ .

$s = \frac{0.0625 + 0 + 0.16 + {(- 0.35)}^{2} + {(4.5 - 5.1)}^{2} + {(5 - 5.1)}^{2} + {(6 - 5.1)}^{2}}{7 - 1}$

Step 7.1.8

Raise $- 0.35$ to the power of $2$ .

$s = \frac{0.0625 + 0 + 0.16 + 0.1225 + {(4.5 - 5.1)}^{2} + {(5 - 5.1)}^{2} + {(6 - 5.1)}^{2}}{7 - 1}$

Step 7.1.9

Subtract $5.1$ from $4.5$ .

$s = \frac{0.0625 + 0 + 0.16 + 0.1225 + {(- 0.6)}^{2} + {(5 - 5.1)}^{2} + {(6 - 5.1)}^{2}}{7 - 1}$

Step 7.1.10

Raise $- 0.6$ to the power of $2$ .

$s = \frac{0.0625 + 0 + 0.16 + 0.1225 + 0.36 + {(5 - 5.1)}^{2} + {(6 - 5.1)}^{2}}{7 - 1}$

Step 7.1.11

Subtract $5.1$ from $5$ .

$s = \frac{0.0625 + 0 + 0.16 + 0.1225 + 0.36 + {(- 0.1)}^{2} + {(6 - 5.1)}^{2}}{7 - 1}$

Step 7.1.12

Raise $- 0.1$ to the power of $2$ .

$s = \frac{0.0625 + 0 + 0.16 + 0.1225 + 0.36 + 0.01 + {(6 - 5.1)}^{2}}{7 - 1}$

Step 7.1.13

Subtract $5.1$ from $6$ .

$s = \frac{0.0625 + 0 + 0.16 + 0.1225 + 0.36 + 0.01 + {0.9}^{2}}{7 - 1}$

Step 7.1.14

Raise $0.9$ to the power of $2$ .

$s = \frac{0.0625 + 0 + 0.16 + 0.1225 + 0.36 + 0.01 + 0.81}{7 - 1}$

Step 7.1.15

Add $0.0625$ and $0$ .

$s = \frac{0.0625 + 0.16 + 0.1225 + 0.36 + 0.01 + 0.81}{7 - 1}$

Step 7.1.16

Add $0.0625$ and $0.16$ .

$s = \frac{0.2225 + 0.1225 + 0.36 + 0.01 + 0.81}{7 - 1}$

Step 7.1.17

Add $0.2225$ and $0.1225$ .

$s = \frac{0.345 + 0.36 + 0.01 + 0.81}{7 - 1}$

Step 7.1.18

Add $0.345$ and $0.36$ .

$s = \frac{0.705 + 0.01 + 0.81}{7 - 1}$

Step 7.1.19

Add $0.705$ and $0.01$ .

$s = \frac{0.715 + 0.81}{7 - 1}$

Step 7.1.20

Add $0.715$ and $0.81$ .

$s = \frac{1.525}{7 - 1}$

Step 7.2

Simplify the expression.

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Step 7.2.1

Subtract $1$ from $7$ .

$s = \frac{1.525}{6}$

Step 7.2.2

Divide $1.525$ by $6$ .

$s = 0.2541\overline{6}$

Step 8

Approximate the result.

$s^{2} \approx 0.2542$