Median of Grouped Data
Grouped data is the data where the class interval frequency and cumulative frequency of the data are given. The median of the grouped data median is calculated using the formula,
Median = l + [(n/2 – cf) / f]×h
where,
- l is Lower Limit of Median Class
- n is Number of Observations
- f is Frequency of Median Class
- h is Class Size
- cf is Cumulative Frequency of Class Preceding Median Class
We can understand the use of the formula by studying the example discussed below,
Example: Find the Median of the following data,
If the marks scored by the students in a class test out of 50 are,
Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
---|---|---|---|---|---|
Number of Students | 5 | 8 | 6 | 6 | 5 |
Solution:
For finding the Median we have to build a table with cumulative frequency as,
Marks 0-10 10-20 20-30 30-40 40-50 Number of Students 5 8 6 6 5 Cumulative Frequency 0+5 = 5 5+8 = 13 13+6 = 19 19+6 = 25 25+5 = 30 n = ∑fi = 5+8+6+6+5 = 30(even)
n/2 = 30/2 = 15
Median Class = 20-30
Now using the formula,
Median = l + [(n/2 – cf) / f]×h
Comparing with the given data we get,
- l = 20
- n = 30
- f = 6
- h = 10
- cf = 13
Median = 20 + [(15 – 10)/6]×10
= 20 + 5/3
= 60/3 + 5/3
= 65/3 = 21.67 (approx)
Thus, the median mark of the class test is 21.67
Median
Median is the middle value of any data when arranged in ascending or descending order. Suppose we have the height of 5 friends as, 171 cm, 174 cm, 167 cm, 169 cm, and 179 cm, then the median height of the friends is calculated as, first arranging the data in ascending order, 167 cm, 169 cm, 171 cm, 174 cm, 179 cm. Now clearly observing the data we see that 171 cm is the middle term in the given data thus, we can say that the median height of the friends is, 171 cm.
In this article, we have covered, median definition, examples of median, median formula and others in detail.
Table of Content
- Median Definition
- Median Formula
- Median of Ungrouped Data
- Median of Grouped Data
- How to Find Median?
- Application of Median Formula