The arranged data can be divided into four equal parts by three values. These values are called quartiles and are denoted by Q1, Q2 and Q3. Here Q1 is first quartile, Q2 is second quartile and Q3 is third quartile.

Calculation of quartiles for ungrouped data

The calculation of quartiles for grouped and ungrouped data is different. In case of ungrouped data, the first, second and third quartiles can be calculated by using the formula:

Problem: The time (in minutes) recorded by a sample of 14 students in a quiz competition is 38, 45, 33, 17, 28, 19, 18, 17, 11, 10, 18, 12, 25, and 40. Find Q1, Q2 and Q3.

Arrange data in ascending order:
10, 11, 12, 17, 17, 18, 18, 19, 25, 28, 33, 38, 40, 45

First Quartile

Q1 can be calculated by using the formula:

Since 3.7th observations lies between 3rd and 4th value in the ordered group, or midway between 12 and 17 therefore

Second Quartile

By using the formula of quartile the calculation of Q2 is given as:

Third Quartile

The calculation of third quartile Q3 is given below:

Calculation of Quartiles for Frequency Distribution

In case of frequency distribution, quartiles can be calculated by using the formula:

Problem: The table below reports the monthly internet charges for a sample of 64 students in the month of January. Find the first, second and third quartiles.

Solution: