Statistics Examples

$- 3$ , $5$ , $2.5$ , $- 0.5$

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.

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

Step 1.2

Simplify the numerator.

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Step 1.2.1

Add $- 3$ and $5$ .

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

Step 1.2.2

Add $2$ and $2.5$ .

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

Step 1.2.3

Subtract $0.5$ from $4.5$ .

$\frac{4}{4}$

Step 1.3

Divide $4$ by $4$ .

$1$

Step 1.4

Divide.

$1$

Step 2

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

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

Step 3

Sum all absolute deviations.

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Step 3.1

Add $4$ and $4$ .

$8 + 1.5 + 1.5$

Step 3.2

Add $8$ and $1.5$ .

$9.5 + 1.5$

Step 3.3

Add $9.5$ and $1.5$ .

$11$

Step 4

Divide the sum by the number of data points.

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Step 4.1

Divide $11$ by $4$ .

$2.75$