Statistics Examples Average Descriptive Statistics

Find the Midhinge

$1$ , $2$ , $3$ , $4$ , $5$

Step 1

There are $5$ observations, so the median is the middle number of the arranged set of data. Splitting the observations either side of the median gives two groups of observations. The median of the lower half of data is the lower or first quartile. The median of the upper half of data is the upper or third quartile.

The median of the lower half of data is the lower or first quartile

The median of the upper half of data is the upper or third quartile

Step 2

Arrange the terms in ascending order.

$1, 2, 3, 4, 5$

Step 3

The median is the middle term in the arranged data set.

$3$

Step 4

The lower half of data is the set below the median.

$1, 2$

Step 5

The median for the lower half of data $1, 2$ is the lower or first quartile. In this case, the first quartile is $1.5$ .

Tap for more steps...

Step 5.1

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.

$\frac{1 + 2}{2}$

Step 5.2

Remove parentheses.

$\frac{1 + 2}{2}$

Step 5.3

Add $1$ and $2$ .

$\frac{3}{2}$

Step 5.4

Convert the median $\frac{3}{2}$ to decimal.

$1.5$

Step 6

The upper half of data is the set above the median.

$4, 5$

Step 7

The median for the upper half of data $4, 5$ is the upper or third quartile. In this case, the third quartile is $4.5$ .

Tap for more steps...

Step 7.1

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.

$\frac{4 + 5}{2}$

Step 7.2

Remove parentheses.

$\frac{4 + 5}{2}$

Step 7.3

Add $4$ and $5$ .

$\frac{9}{2}$

Step 7.4

Convert the median $\frac{9}{2}$ to decimal.

$4.5$

Step 8

The midhinge is the average of the first and third quartiles.

$Midhinge = \frac{Q_{1} + Q_{3}}{2}$

Step 9

Substitute the values for the first quartile $1.5$ and the third quartile $4.5$ into the formula.

$Midhinge = \frac{1.5 + 4.5}{2}$

Step 10

Simplify $\frac{1.5 + 4.5}{2}$ to find the midhinge.

Tap for more steps...

Step 10.1

Add $1.5$ and $4.5$ .

$\frac{6}{2}$

Step 10.2

Divide $6$ by $2$ .

$3$

Enter YOUR Problem

Find the Midhinge

Average Descriptive Statistics

How to Use Step-by-Step Examples

Why use Mathway?

Explore More Statistics Help