Finite Math Examples

$3$ , $3.6$ , $4.32$ , $5.184$

Step 1

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

$\overline{x} = \frac{3 + 3.6 + 4.32 + 5.184}{4}$

Step 2

Simplify the numerator.

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Step 2.1

Add $3$ and $3.6$ .

$\overline{x} = \frac{6.6 + 4.32 + 5.184}{4}$

Step 2.2

Add $6.6$ and $4.32$ .

$\overline{x} = \frac{10.92 + 5.184}{4}$

Step 2.3

Add $10.92$ and $5.184$ .

$\overline{x} = \frac{16.104}{4}$

Step 3

Divide $16.104$ by $4$ .

$\overline{x} = 4.026$

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.

$\overline{x} = 4$

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.

$s = \frac{{(3 - 4)}^{2} + {(3.6 - 4)}^{2} + {(4.32 - 4)}^{2} + {(5.184 - 4)}^{2}}{4 - 1}$

Step 7

Simplify the result.

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Step 7.1

Simplify the numerator.

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Step 7.1.1

Subtract $4$ from $3$ .

$s = \frac{{(- 1)}^{2} + {(3.6 - 4)}^{2} + {(4.32 - 4)}^{2} + {(5.184 - 4)}^{2}}{4 - 1}$

Step 7.1.2

Raise $- 1$ to the power of $2$ .

$s = \frac{1 + {(3.6 - 4)}^{2} + {(4.32 - 4)}^{2} + {(5.184 - 4)}^{2}}{4 - 1}$

Step 7.1.3

Subtract $4$ from $3.6$ .

$s = \frac{1 + {(- 0.4)}^{2} + {(4.32 - 4)}^{2} + {(5.184 - 4)}^{2}}{4 - 1}$

Step 7.1.4

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

$s = \frac{1 + 0.16 + {(4.32 - 4)}^{2} + {(5.184 - 4)}^{2}}{4 - 1}$

Step 7.1.5

Subtract $4$ from $4.32$ .

$s = \frac{1 + 0.16 + {0.32}^{2} + {(5.184 - 4)}^{2}}{4 - 1}$

Step 7.1.6

Raise $0.32$ to the power of $2$ .

$s = \frac{1 + 0.16 + 0.1024 + {(5.184 - 4)}^{2}}{4 - 1}$

Step 7.1.7

Subtract $4$ from $5.184$ .

$s = \frac{1 + 0.16 + 0.1024 + {1.184}^{2}}{4 - 1}$

Step 7.1.8

Raise $1.184$ to the power of $2$ .

$s = \frac{1 + 0.16 + 0.1024 + 1.401856}{4 - 1}$

Step 7.1.9

Add $1$ and $0.16$ .

$s = \frac{1.16 + 0.1024 + 1.401856}{4 - 1}$

Step 7.1.10

Add $1.16$ and $0.1024$ .

$s = \frac{1.2624 + 1.401856}{4 - 1}$

Step 7.1.11

Add $1.2624$ and $1.401856$ .

$s = \frac{2.664256}{4 - 1}$

Step 7.2

Simplify the expression.

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Step 7.2.1

Subtract $1$ from $4$ .

$s = \frac{2.664256}{3}$

Step 7.2.2

Divide $2.664256$ by $3$ .

$s = 0.888085\overline{3}$

Step 8

Approximate the result.

$s^{2} \approx 0.8881$