Statistics Examples

$10$ , $8$ , $2$ , $6$ , $2$

Step 1

Find the mean value.

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Step 1.1

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

$\frac{10 + 8 + 2 + 6 + 2}{5}$

Step 1.2

Simplify the numerator.

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Step 1.2.1

Add $10$ and $8$ .

$\frac{18 + 2 + 6 + 2}{5}$

Step 1.2.2

Add $18$ and $2$ .

$\frac{20 + 6 + 2}{5}$

Step 1.2.3

Add $20$ and $6$ .

$\frac{26 + 2}{5}$

Step 1.2.4

Add $26$ and $2$ .

$\frac{28}{5}$

Step 1.3

Divide.

$5.6$

Step 2

Calculate the distance between each data point and the mean. These are called absolute deviations.

$\begin{array}{c} Data point & Distance from mean \\ 10 & | 10 - 5.6 | = 4.4 \\ 8 & | 8 - 5.6 | = 2.4 \\ 2 & | 2 - 5.6 | = 3.6 \\ 6 & | 6 - 5.6 | = 0.4 \\ 2 & | 2 - 5.6 | = 3.6 \end{array}$

Step 3

Sum all absolute deviations.

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Step 3.1

Add $4.4$ and $2.4$ .

$6.8 + 3.6 + 0.4 + 3.6$

Step 3.2

Add $6.8$ and $3.6$ .

$10.4 + 0.4 + 3.6$

Step 3.3

Add $10.4$ and $0.4$ .

$10.8 + 3.6$

Step 3.4

Add $10.8$ and $3.6$ .

$14.4$

Step 4

Divide the sum by the number of data points.

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Step 4.1

Divide $14.4$ by $5$ .

$2.88$