Quartile: As a measure of central tendency

In statistics, just like, mean, median, mode etc, it is also a measure of central tendency. It is also used to measure dispersion. As the name suggests, divides the data into four quarters. There are many types of these and others are deciles, percentile etc.

Types of quartiles:
There are three types of these and they are as follows:
1. Lower quartile
2. Middle quartile
3. Upper quartile

Lower quartile definition: The first one fourth of the range is called the first quarter. The two end points of this first quarter are the lowest value and the lower quarter. The lower quarter is also called the first quarter. It is denoted by “Q1”. The lower quarter also corresponds to the 25th percentile. It can be calculated using the formula:
L = n*(1/4). Where L = the position of the quarter value. That means that starting from the first number of the data the Lth number would be the first quarter. N = total number of data points.

Middle quarter definition: The middle quarter is also called the median. It divides the data into exactly two halves. Median is a popular measure of central tendency. If there are total n number of observations, then the (n+1)/2 th observation would be the median. Median is denoted by “Q2” or M. The middle quarter corresponds to the 50th percentile.

Upper quartile definition: The upper-quarter divided the range into two parts in the ration 1:3. That means the first 3/4th of the values fall below the upper-quarter and the last 1/4th of the values fall above the upper-quarter. The upper-quarter is also known as the third quarter. It corresponds to 75 percentile. It is denoted by “Q3”.  The formula for calculating the upper-quarter is as follows:
N = n*(3/4). Here, n = number of observations. The Nth observation would be the upper-quarter.

Example: Find the lower, middle and upper-quarter of the following data: 50, 80, 40, 40, 60, 30, 80.
Solution: First we arrange the data in ascending order from the lowest to the highest.
30, 40, 40, 50, 60, 80, 80
Next we locate the middle number. Which, in our example, is 50. So the median = 50.
Now for the lower quarter, we consider the first half of the data only and find the middle number of that. So that would be 40. Lastly the upper quarter would be 80.