Quartiles
There are three quartiles called, first quartile, second quartile and third quartile. There quartiles divides the set of observations into four equal parts. The second quartile is equal to the median. The first quartile is also called lower quartile and is denoted by. The third quartile is also called upper quartile and is denoted by. The lower quartile is a point which has 25% observations less than it and 75% observations are above it. The upper quartile is a point with 75% observations below it and 25% observations above it.
Quartile for Individual Observations (Ungrouped Data):
Quartile for a Frequency Distribution (Discrete Data):
Quartile for Grouped Frequency Distribution:
Example:
The wheat production (in Kg) of 20 acres is given as: 1120, 1240, 1320, 1040, 1080, 1200, 1440, 1360, 1680, 1730, 1785, 1342, 1960, 1880, 1755, 1720, 1600, 1470, 1750, and 1885. Find the quartile deviation and coefficient of quartile deviation.
Solution:
After arranging the observations in ascending order, we get
1040, 1080, 1120, 1200, 1240, 1320, 1342, 1360, 1440, 1470, 1600, 1680, 1720, 1730, 1750, 1755, 1785, 1880, 1885, 1960.
Example:
Calculate the quartile deviation and coefficient of quartile deviation from the data given below:
Maximum Load (shorttons) 
Number of Cables

















Solution:
The necessary calculations are given below:
Maximum Load
(shorttons) 
Number of Cables
() 
Class
Boundaries 
Cumulative
Frequencies 
































lies in the class
Where , , , and
lies in the class
Where , , , and