Statistics Examples

$10$ , $15$ , $15$ , $17$ , $18$ , $21$

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.

$\frac{10 + 15 + 15 + 17 + 18 + 21}{6}$

Step 1.2

Simplify the numerator.

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Step 1.2.1

Add $10$ and $15$ .

$\frac{25 + 15 + 17 + 18 + 21}{6}$

Step 1.2.2

Add $25$ and $15$ .

$\frac{40 + 17 + 18 + 21}{6}$

Step 1.2.3

Add $40$ and $17$ .

$\frac{57 + 18 + 21}{6}$

Step 1.2.4

Add $57$ and $18$ .

$\frac{75 + 21}{6}$

Step 1.2.5

Add $75$ and $21$ .

$\frac{96}{6}$

Step 1.3

Divide $96$ by $6$ .

$16$

Step 2

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

$\begin{array}{c} Data point & Distance from mean \\ 10 & | 10 - 16 | = 6 \\ 15 & | 15 - 16 | = 1 \\ 15 & | 15 - 16 | = 1 \\ 17 & | 17 - 16 | = 1 \\ 18 & | 18 - 16 | = 2 \\ 21 & | 21 - 16 | = 5 \end{array}$

Step 3

Sum all absolute deviations.

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Step 3.1

Add $6$ and $1$ .

$7 + 1 + 1 + 2 + 5$

Step 3.2

Add $7$ and $1$ .

$8 + 1 + 2 + 5$

Step 3.3

Add $8$ and $1$ .

$9 + 2 + 5$

Step 3.4

Add $9$ and $2$ .

$11 + 5$

Step 3.5

Add $11$ and $5$ .

$16$

Step 4

Divide the sum by the number of data points.

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Step 4.1

Divide $16$ by $6$ .

$2.\overline{6}$