Basic Math Examples

$41$ , $45$ , $45$ , $52$ , $64$ , $71$

Step 1

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

$\overline{x} = \frac{41 + 45 + 45 + 52 + 64 + 71}{6}$

Step 2

Simplify the numerator.

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Step 2.1

Add $41$ and $45$ .

$\overline{x} = \frac{86 + 45 + 52 + 64 + 71}{6}$

Step 2.2

Add $86$ and $45$ .

$\overline{x} = \frac{131 + 52 + 64 + 71}{6}$

Step 2.3

Add $131$ and $52$ .

$\overline{x} = \frac{183 + 64 + 71}{6}$

Step 2.4

Add $183$ and $64$ .

$\overline{x} = \frac{247 + 71}{6}$

Step 2.5

Add $247$ and $71$ .

$\overline{x} = \frac{318}{6}$

Step 3

Divide $318$ by $6$ .

$\overline{x} = 53$

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.

$s = \frac{{(41 - 53)}^{2} + {(45 - 53)}^{2} + {(45 - 53)}^{2} + {(52 - 53)}^{2} + {(64 - 53)}^{2} + {(71 - 53)}^{2}}{6 - 1}$

Step 6

Simplify the result.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Subtract $53$ from $41$ .

$s = \frac{{(- 12)}^{2} + {(45 - 53)}^{2} + {(45 - 53)}^{2} + {(52 - 53)}^{2} + {(64 - 53)}^{2} + {(71 - 53)}^{2}}{6 - 1}$

Step 6.1.2

Raise $- 12$ to the power of $2$ .

$s = \frac{144 + {(45 - 53)}^{2} + {(45 - 53)}^{2} + {(52 - 53)}^{2} + {(64 - 53)}^{2} + {(71 - 53)}^{2}}{6 - 1}$

Step 6.1.3

Subtract $53$ from $45$ .

$s = \frac{144 + {(- 8)}^{2} + {(45 - 53)}^{2} + {(52 - 53)}^{2} + {(64 - 53)}^{2} + {(71 - 53)}^{2}}{6 - 1}$

Step 6.1.4

Raise $- 8$ to the power of $2$ .

$s = \frac{144 + 64 + {(45 - 53)}^{2} + {(52 - 53)}^{2} + {(64 - 53)}^{2} + {(71 - 53)}^{2}}{6 - 1}$

Step 6.1.5

Subtract $53$ from $45$ .

$s = \frac{144 + 64 + {(- 8)}^{2} + {(52 - 53)}^{2} + {(64 - 53)}^{2} + {(71 - 53)}^{2}}{6 - 1}$

Step 6.1.6

Raise $- 8$ to the power of $2$ .

$s = \frac{144 + 64 + 64 + {(52 - 53)}^{2} + {(64 - 53)}^{2} + {(71 - 53)}^{2}}{6 - 1}$

Step 6.1.7

Subtract $53$ from $52$ .

$s = \frac{144 + 64 + 64 + {(- 1)}^{2} + {(64 - 53)}^{2} + {(71 - 53)}^{2}}{6 - 1}$

Step 6.1.8

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

$s = \frac{144 + 64 + 64 + 1 + {(64 - 53)}^{2} + {(71 - 53)}^{2}}{6 - 1}$

Step 6.1.9

Subtract $53$ from $64$ .

$s = \frac{144 + 64 + 64 + 1 + 11^{2} + {(71 - 53)}^{2}}{6 - 1}$

Step 6.1.10

Raise $11$ to the power of $2$ .

$s = \frac{144 + 64 + 64 + 1 + 121 + {(71 - 53)}^{2}}{6 - 1}$

Step 6.1.11

Subtract $53$ from $71$ .

$s = \frac{144 + 64 + 64 + 1 + 121 + 18^{2}}{6 - 1}$

Step 6.1.12

Raise $18$ to the power of $2$ .

$s = \frac{144 + 64 + 64 + 1 + 121 + 324}{6 - 1}$

Step 6.1.13

Add $144$ and $64$ .

$s = \frac{208 + 64 + 1 + 121 + 324}{6 - 1}$

Step 6.1.14

Add $208$ and $64$ .

$s = \frac{272 + 1 + 121 + 324}{6 - 1}$

Step 6.1.15

Add $272$ and $1$ .

$s = \frac{273 + 121 + 324}{6 - 1}$

Step 6.1.16

Add $273$ and $121$ .

$s = \frac{394 + 324}{6 - 1}$

Step 6.1.17

Add $394$ and $324$ .

$s = \frac{718}{6 - 1}$

Step 6.2

Subtract $1$ from $6$ .

$s = \frac{718}{5}$

Step 7

Approximate the result.

$s^{2} \approx 143.6$