Statistics Examples

3

$3$ ,

4

$4$ ,

5

$5$ ,

12

$12$

Step 1

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

μ = \frac{3 + 4 + 5 + 12}{4}

$μ = \frac{3 + 4 + 5 + 12}{4}$

Step 2

Simplify the numerator.

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Step 2.1

Add

3

$3$ and

4

$4$ .

μ = \frac{7 + 5 + 12}{4}

$μ = \frac{7 + 5 + 12}{4}$

Step 2.2

Add

7

$7$ and

5

$5$ .

μ = \frac{12 + 12}{4}

$μ = \frac{12 + 12}{4}$

Step 2.3

Add

12

$12$ and

12

$12$ .

μ = \frac{24}{4}

$μ = \frac{24}{4}$

μ = \frac{24}{4}

$μ = \frac{24}{4}$

Step 3

Divide

24

$24$ by

4

$4$ .

μ = 6

$μ = 6$

Step 4

Arrange the terms in ascending order.

M e d i a n = 3, 4, 5, 12

$M e d i a n = 3, 4, 5, 12$

Step 5

The median is the middle term in the arranged data set. In the case of an even number of terms, the median is the average of the two middle terms.

M e d i a n = \frac{4 + 5}{2}

$M e d i a n = \frac{4 + 5}{2}$

Step 6

Remove parentheses.

M e d i a n = \frac{4 + 5}{2}

$M e d i a n = \frac{4 + 5}{2}$

Step 7

Add

4

$4$ and

5

$5$ .

M e d i a n = \frac{9}{2}

$M e d i a n = \frac{9}{2}$

Step 8

Convert the median

\frac{9}{2}

$\frac{9}{2}$ to decimal.

M e d i a n = 4.5

$M e d i a n = 4.5$

Step 9

Since the mean is greater than the median, the data set is positively skewed.

Positively Skewed

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