Quartile

Quartile

A statistical term describing a division of observation based upon the values of the data is called quartile. The middle number between the lowest number and the median of the data set is first quartile (Q₁), the median of the data is second quartile (Q₂) and the middle value between the median and the highest value of the data set is third quartile (Q₃).

The lower quartile(Q₁) is a point which has 25% observation below it and 75% observations above it. The upper quartile (Q₃) is a point of 75% observation below it and 25% observation above it.

Note:

The quartiles divide the set of measurements into four equal parts. Twenty-five percent of the measurements are less than the lower quartile, fifty percent of the measurements are less than the median and seventy-five percent of the measurements are less than the upper quartiles So, fifty percent of the measurements are between the lower quartile and the upper quartile.

Example

Find the quartiles of the list:

10, 8, 6, 4, 12, 18, 20

Solution:

We need to put the given list in order:

4, 6, 8,1 0, 12,1 8, 20

First, we cut the list in half by finding the median.

The middle number is 10.

so, the median = 10

Now we look at the left half of the list (not including the median):

4, 6, 8 and we find its median.

Median of the left half = 6

Finally, we look at the right half of the list:

12, 18, 20 and we find its median

12, 18, 20 and we find its median. Median of the right half = 18

The quartiles are 6, 10, 18