Lower Quartile

Introduction to lower quartile:

In descriptive statistics, a quartile is any of the three values which divide the sorted data set into four equal parts, so that each part represents one fourth of the sampled population. Lower Quartile is one type of quantile.In that quartile, the 25 % of data which lie in the lower half of the data set is called as lower quartile. We can also define it as the middle value of the lower half.

For example,

21, 5, 22, 33, 17, 36, 14, 42, 15, 35, 27


Arrange the data in ascending order,

5, 14, 15, 17, 21, 22, 27, 33, 35, 36, 42

In the above Data set,

15 is lower quartile.

Calculation of Lower Quartile:

Lower Quartile for Odd data set:

Let us see how to calculate the lower quartile of the data set that contains odd numbers.

Step1:  First find the median of the data set. The median divide the data set into upper and lower part.

Step2:  Find the median for lower part of the data set .That median is called as lower quartile.                    

Ex: Data Set: 8, 49, 53, 19, 45, 44, 11, 41, 47, 51, 39

Ordered Data set: 8, 11, 19, 39, 41, 44, 45, 47,49,51,53

Median (Mid value) =44

Lower part = 8, 11, 19, 39, 41

Upper part = 45, 47,49,51,53

Lower quartile (Median of lower part) = 19

Lower Quartile for Even Data set:

Let us see how to calculate the lower quartile of the data set that contains even numbers.

Step 1: Find the Median of the data set by calculating the average of the data set.

Step 2: Next in the lower part, find the median by calculating the average. That value is known as lower quartile.

Ex: Data set: 13, 6, 24, 33, 9, 38, 16, 46, 19, 53, 26, 65

Ordered data set: 6,9,13,16,19,24,26,33,38,46,53,65

Median: (24+26)/2= 25

Lower quartile:  (24+33)/2= 28.5



Practice Problems on Lower Quartile

Find the lower Quartile for the following;

1.   17,11,47,27,69,20,6,34,12,93,33

2.   7,4,18,23,30,20,14,36,41,11,48,64

Answer Key:

1.12

2.12.5