An Introduction to Quartiles in Statistics

Quartile is a term derived from the word ‘quarter’ which is one fourth of something. So, we can say  Quartiles Statistics is a certain fourth of a data set. When a given data is arranged in the ascending order that is from the lowest value to the highest value and this data is divided into groups of four, we get what we call Statistics Quartiles.

In Quartiles Statistics there are three quartiles which are, the first quartile also called as lower quartile is denoted as Q1 which lies in the twenty five percent of the bottom data. The second quartile is the median of the data that divides the data in the middle and has fifty percent of the data below it and the other fifty percent of the data above it. It is denoted as Q2.The third quartile also called the upper quartile denoted as Q3 has seventy five percent of the data below it and twenty five percent of the data above it.

We can state the Quartiles Definition as, Quartiles are the three values that divide an ordered data set into four approximately equal parts. Definition of Quartiles can also be given as, A statistical term describing a division of a data set into four defined intervals based upon the values of the data and how they compare the entire data set.

Now that we are a bit familiar with Quartiles Statistics, let us learn how to calculate Quartiles of a given data set. For a better understanding of the steps involved let us consider a data set. Calculate the three
 quartiles of the data set of scores,  27 18 20 20 23 29 24.

The steps involved are:
• Count the total number of scores in the given data; n= 7
• Arrange the data set of scores in the ascending order, that is, from the lowest score to the highest score, we get, 18 20, 20, 23, 24, 27, 29
• Find the median (Q2) which is the middle value of the data set
Median = ½(n+1) = ½(7+1)= 4
So, the median (Q2)=23 [the fourth term of the ordered data set]
• Next we shall calculate the lower quartile (Q1) which is the median of the lower half of the data set.    Q1 = ¼(n+1) = ¼(7+1) = 2
So, the lower quartile (Q1) = 20 [the second term of the ordered data set]
• Finally we shall calculate the upper quartile (Q3) which is the median of the upper half of the data set. Q3=3/4(n+1) = ¾(7+1) = 6
So, the upper quartile (Q3)= 27 [the sixth term of the ordered data set]

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