Basic Math Examples

$10$ , $11$ , $12$ , $12$ , $13$ , $13$ , $13$ , $14$ , $14$ , $14$ , $15$ , $15$ , $15$ , $15$ , $15$ , $16$ , $16$ , $16$ , $17$ , $17$ , $17$ , $17$ , $18$ , $18$ , $25$

Step 1

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

$\overline{x} = \frac{10 + 11 + 12 + 12 + 13 + 13 + 13 + 14 + 14 + 14 + 15 + 15 + 15 + 15 + 15 + 16 + 16 + 16 + 17 + 17 + 17 + 17 + 18 + 18 + 25}{25}$

Step 2

Simplify the numerator.

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Step 2.1

Add $10$ and $11$ .

$\overline{x} = \frac{21 + 12 + 12 + 13 + 13 + 13 + 14 + 14 + 14 + 15 + 15 + 15 + 15 + 15 + 16 + 16 + 16 + 17 + 17 + 17 + 17 + 18 + 18 + 25}{25}$

Step 2.2

Add $21$ and $12$ .

$\overline{x} = \frac{33 + 12 + 13 + 13 + 13 + 14 + 14 + 14 + 15 + 15 + 15 + 15 + 15 + 16 + 16 + 16 + 17 + 17 + 17 + 17 + 18 + 18 + 25}{25}$

Step 2.3

Add $33$ and $12$ .

$\overline{x} = \frac{45 + 13 + 13 + 13 + 14 + 14 + 14 + 15 + 15 + 15 + 15 + 15 + 16 + 16 + 16 + 17 + 17 + 17 + 17 + 18 + 18 + 25}{25}$

Step 2.4

Add $45$ and $13$ .

$\overline{x} = \frac{58 + 13 + 13 + 14 + 14 + 14 + 15 + 15 + 15 + 15 + 15 + 16 + 16 + 16 + 17 + 17 + 17 + 17 + 18 + 18 + 25}{25}$

Step 2.5

Add $58$ and $13$ .

$\overline{x} = \frac{71 + 13 + 14 + 14 + 14 + 15 + 15 + 15 + 15 + 15 + 16 + 16 + 16 + 17 + 17 + 17 + 17 + 18 + 18 + 25}{25}$

Step 2.6

Add $71$ and $13$ .

$\overline{x} = \frac{84 + 14 + 14 + 14 + 15 + 15 + 15 + 15 + 15 + 16 + 16 + 16 + 17 + 17 + 17 + 17 + 18 + 18 + 25}{25}$

Step 2.7

Add $84$ and $14$ .

$\overline{x} = \frac{98 + 14 + 14 + 15 + 15 + 15 + 15 + 15 + 16 + 16 + 16 + 17 + 17 + 17 + 17 + 18 + 18 + 25}{25}$

Step 2.8

Add $98$ and $14$ .

$\overline{x} = \frac{112 + 14 + 15 + 15 + 15 + 15 + 15 + 16 + 16 + 16 + 17 + 17 + 17 + 17 + 18 + 18 + 25}{25}$

Step 2.9

Add $112$ and $14$ .

$\overline{x} = \frac{126 + 15 + 15 + 15 + 15 + 15 + 16 + 16 + 16 + 17 + 17 + 17 + 17 + 18 + 18 + 25}{25}$

Step 2.10

Add $126$ and $15$ .

$\overline{x} = \frac{141 + 15 + 15 + 15 + 15 + 16 + 16 + 16 + 17 + 17 + 17 + 17 + 18 + 18 + 25}{25}$

Step 2.11

Add $141$ and $15$ .

$\overline{x} = \frac{156 + 15 + 15 + 15 + 16 + 16 + 16 + 17 + 17 + 17 + 17 + 18 + 18 + 25}{25}$

Step 2.12

Add $156$ and $15$ .

$\overline{x} = \frac{171 + 15 + 15 + 16 + 16 + 16 + 17 + 17 + 17 + 17 + 18 + 18 + 25}{25}$

Step 2.13

Add $171$ and $15$ .

$\overline{x} = \frac{186 + 15 + 16 + 16 + 16 + 17 + 17 + 17 + 17 + 18 + 18 + 25}{25}$

Step 2.14

Add $186$ and $15$ .

$\overline{x} = \frac{201 + 16 + 16 + 16 + 17 + 17 + 17 + 17 + 18 + 18 + 25}{25}$

Step 2.15

Add $201$ and $16$ .

$\overline{x} = \frac{217 + 16 + 16 + 17 + 17 + 17 + 17 + 18 + 18 + 25}{25}$

Step 2.16

Add $217$ and $16$ .

$\overline{x} = \frac{233 + 16 + 17 + 17 + 17 + 17 + 18 + 18 + 25}{25}$

Step 2.17

Add $233$ and $16$ .

$\overline{x} = \frac{249 + 17 + 17 + 17 + 17 + 18 + 18 + 25}{25}$

Step 2.18

Add $249$ and $17$ .

$\overline{x} = \frac{266 + 17 + 17 + 17 + 18 + 18 + 25}{25}$

Step 2.19

Add $266$ and $17$ .

$\overline{x} = \frac{283 + 17 + 17 + 18 + 18 + 25}{25}$

Step 2.20

Add $283$ and $17$ .

$\overline{x} = \frac{300 + 17 + 18 + 18 + 25}{25}$

Step 2.21

Add $300$ and $17$ .

$\overline{x} = \frac{317 + 18 + 18 + 25}{25}$

Step 2.22

Add $317$ and $18$ .

$\overline{x} = \frac{335 + 18 + 25}{25}$

Step 2.23

Add $335$ and $18$ .

$\overline{x} = \frac{353 + 25}{25}$

Step 2.24

Add $353$ and $25$ .

$\overline{x} = \frac{378}{25}$

Step 3

Divide.

$\overline{x} = 15.12$

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.

$\overline{x} = 15.1$

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.

$s = \frac{{(10 - 15.1)}^{2} + {(11 - 15.1)}^{2} + {(12 - 15.1)}^{2} + {(12 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(25 - 15.1)}^{2}}{25 - 1}$

Step 7

Simplify the result.

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Step 7.1

Simplify the numerator.

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Step 7.1.1

Subtract $15.1$ from $10$ .

$s = \frac{{(- 5.1)}^{2} + {(11 - 15.1)}^{2} + {(12 - 15.1)}^{2} + {(12 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(25 - 15.1)}^{2}}{25 - 1}$

Step 7.1.2

Raise $- 5.1$ to the power of $2$ .

$s = \frac{26.01 + {(11 - 15.1)}^{2} + {(12 - 15.1)}^{2} + {(12 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(25 - 15.1)}^{2}}{25 - 1}$

Step 7.1.3

Subtract $15.1$ from $11$ .

$s = \frac{26.01 + {(- 4.1)}^{2} + {(12 - 15.1)}^{2} + {(12 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(25 - 15.1)}^{2}}{25 - 1}$

Step 7.1.4

Raise $- 4.1$ to the power of $2$ .

$s = \frac{26.01 + 16.81 + {(12 - 15.1)}^{2} + {(12 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(25 - 15.1)}^{2}}{25 - 1}$

Step 7.1.5

Subtract $15.1$ from $12$ .

$s = \frac{26.01 + 16.81 + {(- 3.1)}^{2} + {(12 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(25 - 15.1)}^{2}}{25 - 1}$

Step 7.1.6

Raise $- 3.1$ to the power of $2$ .

$s = \frac{26.01 + 16.81 + 9.61 + {(12 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(25 - 15.1)}^{2}}{25 - 1}$

Step 7.1.7

Subtract $15.1$ from $12$ .

$s = \frac{26.01 + 16.81 + 9.61 + {(- 3.1)}^{2} + {(13 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(25 - 15.1)}^{2}}{25 - 1}$

Step 7.1.8

Raise $- 3.1$ to the power of $2$ .

$s = \frac{26.01 + 16.81 + 9.61 + 9.61 + {(13 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(25 - 15.1)}^{2}}{25 - 1}$

Step 7.1.9

Subtract $15.1$ from $13$ .

$s = \frac{26.01 + 16.81 + 9.61 + 9.61 + {(- 2.1)}^{2} + {(13 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(25 - 15.1)}^{2}}{25 - 1}$

Step 7.1.10

Raise $- 2.1$ to the power of $2$ .

$s = \frac{26.01 + 16.81 + 9.61 + 9.61 + 4.41 + {(13 - 15.1)}^{2} + {(13 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(25 - 15.1)}^{2}}{25 - 1}$

Step 7.1.11

Subtract $15.1$ from $13$ .

$s = \frac{26.01 + 16.81 + 9.61 + 9.61 + 4.41 + {(- 2.1)}^{2} + {(13 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(25 - 15.1)}^{2}}{25 - 1}$

Step 7.1.12

Raise $- 2.1$ to the power of $2$ .

$s = \frac{26.01 + 16.81 + 9.61 + 9.61 + 4.41 + 4.41 + {(13 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(25 - 15.1)}^{2}}{25 - 1}$

Step 7.1.13

Subtract $15.1$ from $13$ .

$s = \frac{26.01 + 16.81 + 9.61 + 9.61 + 4.41 + 4.41 + {(- 2.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(25 - 15.1)}^{2}}{25 - 1}$

Step 7.1.14

Raise $- 2.1$ to the power of $2$ .

$s = \frac{26.01 + 16.81 + 9.61 + 9.61 + 4.41 + 4.41 + 4.41 + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(25 - 15.1)}^{2}}{25 - 1}$

Step 7.1.15

Subtract $15.1$ from $14$ .

$s = \frac{26.01 + 16.81 + 9.61 + 9.61 + 4.41 + 4.41 + 4.41 + {(- 1.1)}^{2} + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(25 - 15.1)}^{2}}{25 - 1}$

Step 7.1.16

Raise $- 1.1$ to the power of $2$ .

$s = \frac{26.01 + 16.81 + 9.61 + 9.61 + 4.41 + 4.41 + 4.41 + 1.21 + {(14 - 15.1)}^{2} + {(14 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(25 - 15.1)}^{2}}{25 - 1}$

Step 7.1.17

Subtract $15.1$ from $14$ .

$s = \frac{26.01 + 16.81 + 9.61 + 9.61 + 4.41 + 4.41 + 4.41 + 1.21 + {(- 1.1)}^{2} + {(14 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(25 - 15.1)}^{2}}{25 - 1}$

Step 7.1.18

Raise $- 1.1$ to the power of $2$ .

$s = \frac{26.01 + 16.81 + 9.61 + 9.61 + 4.41 + 4.41 + 4.41 + 1.21 + 1.21 + {(14 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(25 - 15.1)}^{2}}{25 - 1}$

Step 7.1.19

Subtract $15.1$ from $14$ .

$s = \frac{26.01 + 16.81 + 9.61 + 9.61 + 4.41 + 4.41 + 4.41 + 1.21 + 1.21 + {(- 1.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(25 - 15.1)}^{2}}{25 - 1}$

Step 7.1.20

Raise $- 1.1$ to the power of $2$ .

$s = \frac{26.01 + 16.81 + 9.61 + 9.61 + 4.41 + 4.41 + 4.41 + 1.21 + 1.21 + 1.21 + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(25 - 15.1)}^{2}}{25 - 1}$

Step 7.1.21

Subtract $15.1$ from $15$ .

$s = \frac{26.01 + 16.81 + 9.61 + 9.61 + 4.41 + 4.41 + 4.41 + 1.21 + 1.21 + 1.21 + {(- 0.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(15 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(16 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(17 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(18 - 15.1)}^{2} + {(25 - 15.1)}^{2}}{25 - 1}$

Step 7.1.22