Finite Math Examples

$20$ , $12$ , $6$ , $7$ , $11$

Step 1

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

$\overline{x} = \frac{20 + 12 + 6 + 7 + 11}{5}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Add $20$ and $12$ .

$\overline{x} = \frac{32 + 6 + 7 + 11}{5}$

Step 2.2

Add $32$ and $6$ .

$\overline{x} = \frac{38 + 7 + 11}{5}$

Step 2.3

Add $38$ and $7$ .

$\overline{x} = \frac{45 + 11}{5}$

Step 2.4

Add $45$ and $11$ .

$\overline{x} = \frac{56}{5}$

Step 3

Divide.

$\overline{x} = 11.2$

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.

$s = \frac{{(20 - 11.2)}^{2} + {(12 - 11.2)}^{2} + {(6 - 11.2)}^{2} + {(7 - 11.2)}^{2} + {(11 - 11.2)}^{2}}{5 - 1}$

Step 6

Simplify the result.

Tap for more steps...

Step 6.1

Simplify the numerator.

Tap for more steps...

Step 6.1.1

Subtract $11.2$ from $20$ .

$s = \frac{{8.8}^{2} + {(12 - 11.2)}^{2} + {(6 - 11.2)}^{2} + {(7 - 11.2)}^{2} + {(11 - 11.2)}^{2}}{5 - 1}$

Step 6.1.2

Raise $8.8$ to the power of $2$ .

$s = \frac{77.44 + {(12 - 11.2)}^{2} + {(6 - 11.2)}^{2} + {(7 - 11.2)}^{2} + {(11 - 11.2)}^{2}}{5 - 1}$

Step 6.1.3

Subtract $11.2$ from $12$ .

$s = \frac{77.44 + {0.8}^{2} + {(6 - 11.2)}^{2} + {(7 - 11.2)}^{2} + {(11 - 11.2)}^{2}}{5 - 1}$

Step 6.1.4

Raise $0.8$ to the power of $2$ .

$s = \frac{77.44 + 0.64 + {(6 - 11.2)}^{2} + {(7 - 11.2)}^{2} + {(11 - 11.2)}^{2}}{5 - 1}$

Step 6.1.5

Subtract $11.2$ from $6$ .

$s = \frac{77.44 + 0.64 + {(- 5.2)}^{2} + {(7 - 11.2)}^{2} + {(11 - 11.2)}^{2}}{5 - 1}$

Step 6.1.6

Raise $- 5.2$ to the power of $2$ .

$s = \frac{77.44 + 0.64 + 27.04 + {(7 - 11.2)}^{2} + {(11 - 11.2)}^{2}}{5 - 1}$

Step 6.1.7

Subtract $11.2$ from $7$ .

$s = \frac{77.44 + 0.64 + 27.04 + {(- 4.2)}^{2} + {(11 - 11.2)}^{2}}{5 - 1}$

Step 6.1.8

Raise $- 4.2$ to the power of $2$ .

$s = \frac{77.44 + 0.64 + 27.04 + 17.64 + {(11 - 11.2)}^{2}}{5 - 1}$

Step 6.1.9

Subtract $11.2$ from $11$ .

$s = \frac{77.44 + 0.64 + 27.04 + 17.64 + {(- 0.2)}^{2}}{5 - 1}$

Step 6.1.10

Raise $- 0.2$ to the power of $2$ .

$s = \frac{77.44 + 0.64 + 27.04 + 17.64 + 0.04}{5 - 1}$

Step 6.1.11

Add $77.44$ and $0.64$ .

$s = \frac{78.08 + 27.04 + 17.64 + 0.04}{5 - 1}$

Step 6.1.12

Add $78.08$ and $27.04$ .

$s = \frac{105.12 + 17.64 + 0.04}{5 - 1}$

Step 6.1.13

Add $105.12$ and $17.64$ .

$s = \frac{122.76 + 0.04}{5 - 1}$

Step 6.1.14

Add $122.76$ and $0.04$ .

$s = \frac{122.8}{5 - 1}$

Step 6.2

Simplify the expression.

Tap for more steps...

Step 6.2.1

Subtract $1$ from $5$ .

$s = \frac{122.8}{4}$

Step 6.2.2

Divide $122.8$ by $4$ .

$s = 30.7$

Step 7

Approximate the result.

$s^{2} \approx 30.7$