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
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
By using the formula of quartile the calculation of Q2 is given as:
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.
In case of frequency distribution first quartile can be calculated by using the formula given below:
The calculation of second quartile is given below:
Like first and second quartile, the calculation of third quartile is given as: