Statistics Examples

10

$10$ ,

15

$15$ ,

15

$15$ ,

17

$17$ ,

18

$18$ ,

21

$21$

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}

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

Step 1.2

Simplify the numerator.

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Step 1.2.1

Add

10

$10$ and

15

$15$ .

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

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

Step 1.2.2

Add

25

$25$ and

15

$15$ .

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

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

Step 1.2.3

Add

40

$40$ and

17

$17$ .

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

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

Step 1.2.4

Add

57

$57$ and

18

$18$ .

\frac{75 + 21}{6}

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

Step 1.2.5

Add

75

$75$ and

21

$21$ .

\frac{96}{6}

$\frac{96}{6}$

\frac{96}{6}

$\frac{96}{6}$

Step 1.3

Divide

96

$96$ by

6

$6$ .

16

$16$

16

$16$

Step 2

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

\begin{matrix} 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{matrix}

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

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

$6$ .

$2.\overline{6}$

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