Statistics Examples

- 3

$- 3$ ,

5

$5$ ,

2.5

$2.5$ ,

- 0.5

$- 0.5$

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{- 3 + 5 + 2.5 - 0.5}{4}

$\frac{- 3 + 5 + 2.5 - 0.5}{4}$

Step 1.2

Simplify the numerator.

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Step 1.2.1

Add

- 3

$- 3$ and

5

$5$ .

\frac{2 + 2.5 - 0.5}{4}

$\frac{2 + 2.5 - 0.5}{4}$

Step 1.2.2

Add

2

$2$ and

2.5

$2.5$ .

\frac{4.5 - 0.5}{4}

$\frac{4.5 - 0.5}{4}$

Step 1.2.3

Subtract

0.5

$0.5$ from

4.5

$4.5$ .

\frac{4}{4}

$\frac{4}{4}$

\frac{4}{4}

$\frac{4}{4}$

Step 1.3

Divide

4

$4$ by

4

$4$ .

1

$1$

Step 1.4

Divide.

1

$1$

1

$1$

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 \\ - 3 & | - 3 - 1 | = 4 \\ 5 & | 5 - 1 | = 4 \\ 2.5 & | 2.5 - 1 | = 1.5 \\ - 0.5 & | - 0.5 - 1 | = 1.5 \end{array}

$\begin{array}{c} Data point & Distance from mean \\ - 3 & | - 3 - 1 | = 4 \\ 5 & | 5 - 1 | = 4 \\ 2.5 & | 2.5 - 1 | = 1.5 \\ - 0.5 & | - 0.5 - 1 | = 1.5 \end{array}$

Step 3

Sum all absolute deviations.

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Step 3.1

Add

4

$4$ and

4

$4$ .

8 + 1.5 + 1.5

$8 + 1.5 + 1.5$

Step 3.2

Add

8

$8$ and

1.5

$1.5$ .

9.5 + 1.5

$9.5 + 1.5$

Step 3.3

Add

9.5

$9.5$ and

1.5

$1.5$ .

11

$11$

11

$11$

Step 4

Divide the sum by the number of data points.

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Step 4.1

Divide

11

$11$ by

4

$4$ .

2.75

$2.75$

2.75

$2.75$

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