How to Find Quartiles of Continuous Data?

posted in: Descriptive Statistics | updated on: 25 Sep, 2012

When we have a Set of Numbers that are being evaluated statistically then we must know certain values that can be significant for this purpose. We can have many such values like the smallest value, largest value, median and the lower & upper quartiles. The lower quartile splits the 1st 25 % of data set and the rest i.e. 75 % of the set. Similarly, upper quartile splits the last 25 % of the data set and rest beginning portion of 75 % of the set. It is easy to find out the lower and upper quartiles. So, let us learn how to find quartiles of continuous data with help of an example:

Example: Suppose we have the following data set:
 

Class Interval	Frequency
10 – 20	2
20 – 30	4
30 – 40	2
40 – 50	4

 
 Find the lower and the upper quartiles of the above continuous data?

Solution: First we determine the class marks and cumulative frequencies as follows:
 

Class Interval	Class marks	Frequency	Cumulative Frequency
10 – 20	15	2	2
20 – 30	25	4	6
30 – 40	35	2	8
40 – 50	45	4	12

 

We then find the Median as: sum of frequencies /2 = 12 /2 = 6,

So, our median class is: 30 – 40. The value of median will be evaluated as:

M = 30 + (6 – 6)/4 * 10 = 30,

Next we determine smallest and largest values in the data set:

Smallest Value: 15 and,

Largest value: 45,

To find the lower quartile: (15 + 30) /2 = 45 /2 = 22.5,

To find the upper quartile: (45 + 30) /2 = 75 /2 = 37.5,

Thus we get the values for upper and lower quartiles as 37.5 and 22.5 respectively.