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Introduction to Quartile for Grouped Data:

Dividing the whole grouped data into four equal parts by three divisions is called as quartiles. The main three divisions are as follows median, lower quartile, and upper quartile. Find the median for a given set of grouped data. Finding the middle value for first number and the median value is known as lower quartile. Finding the middle value for median value and the last number in a given set is known as upper quartile. Difference of upper quartile and the lower quartile is called as inter-quartile range for grouped data. Let us see about quartile for grouped data in this article.

Formula - Quartile for Grouped Data

Formula for all the quartile of grouped data is given:

n - n is the total number of elements in a set.

Median = (n + 1)/2 = Q_2 = fiftieth percentile.

Lower quartile = (n + 1)/4= Q_1 = twenty-fifth percentile.

Upper quartile = (3(n + 1 ))/4 = Q_3 = seventy-fifth percentile.

Inter-quartile range (IQR) = upper quartile lower quartile.

Worked Examples to Quartile for Grouped Data

Example 1 to Quartile for Grouped Data:

Find all of the quartiles for the given grouped data 22, 23, 24, 25, 36, 27, 28, 20, 33, 34, 35, 37, 38, 39, and 40.

Solution:

Step 1:

Given grouped data is 22, 23, 24, 25, 36, 27, 28, 20, 33, 34, 35, 37, 38, 39, and 40.

Step 2:

Write the given set of data in ascending order.

20, 22, 23, 24, 25, 27, 28, 33, 34, 35, 36, 37, 38, 39, and 40

Step 3:

Total number of elements in a set is n = 15

The median is (n + 1)/2 = (15 + 1)/2 = 16/2 = 8

The 8th element is the median element.

Therefore, Median value is 33.

Step 4:

Lower quartile = (n + 1)/4 = (15 + 1)/4 = 16/4 = 4

The 4th element is the lower quartile element.

Therefore, the lower quartile value is 24.

Step 5:

Upper quartile = (3(n + 1)/4 = (3 (15 + 1))/4 = 3(16)/4 = 48/4 = 12

The 12th element is the upper quartile.

Therefore, the upper quartile value is 37.

Step 6:

Upper Quartile = 37

Lower Quartile = 24

From the above find the inter-quartile range,

Formula for inter-quartile range is = upper quartile - lower quartile.

= 37 24

= 13

Therefore, the inter-quartile range value is 13.

Example 2 to Quartile for Grouped Data:

Find all of the quartiles for the given grouped data 10, 12, 13, 14, 17, 13, 12, 15, 16, 18, 19, 20, 21, 18, 19, 21, 22, 24, 26, 27, 28, 29, 30.

Solution:

Step 1:

Given grouped data is 10, 12, 13, 14, 17, 13, 12, 15, 16, 18, 19, 20, 21, 18, 19, 21, 22, 24, 26, 27, 28, 29, and 30.

Step 2:

Write the given set of data in ascending order.

10, 12, 12, 13, 13, 14, 15, 16, 17, 18, 18, 19, 19, 20, 21, 21, 22, 24, 26, 27, 28, 29, and 30

Step 3:

Total number of elements in a set is n = 23

The median is (n + 1)/2 = (23 + 1)/2 = 24/2 = 12

The 12th element is the median element.

Therefore, Median value is 19.

Step 4:

Lower quartile = (n + 1)/4 = (23 + 1)/4 = 24/4 = 6

The 6th element is the lower quartile element.

Therefore, the lower quartile value is 14.

Step 5:

Upper quartile = (3(n + 1)/4 = (3 (23 + 1))/4 = 3(24)/4 = 72/4 = 18

The 18th element is the upper quartile.

Therefore, the upper quartile value is 24.

Step 6:

Upper Quartile = 24

Lower Quartile = 14

From the above find the inter-quartile range,

Formula for inter-quartile range is = upper quartile - lower quartile.

= 24 14

= 10

Therefore, the inter-quartile range value is 10.

by: Omkar Nayak

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