Solved Examples on Median
Example 1: Find the median of the given data set 60, 70, 10, 30, and 50
Solution:
Median of the data 60, 70, 10, 30, and 50 is,
Step 1: Order the given data in ascending order as:
10, 30, 50, 60, 70
Step 2: Check if n (number of terms of data set) is even or odd and find the median of the data with respective ‘n’ value.
Step 3: Here, n = 5 (odd)
Median = [(n + 1)/2]th term
Median = [(5 + 1)/2]th term = 3rd term
= 50
Example 2: Find the median of the given data set 13, 47, 19, 25, 75, 66, and 50
Solution:
Median of the data 13, 47, 19, 25, 75, 66, and 50 is,
Step 1: Order the given data in ascending order as:
13, 19, 25, 47, 50, 66, 75
Step 2: Check if n (number of terms of data set) is even or odd and find the median of the data with respective ‘n’ value.
Step 3: Here, n = 7 (odd)
Median = [(n + 1)/2]th term
Median = [(7 + 1)/2]th term = 4th term
= 47
Example 3: Find the Median of the following data,
If the marks scored by the students in a class test out of 100 are,
Marks | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 |
---|---|---|---|---|---|
Number of Students | 5 | 7 | 9 | 4 | 5 |
Solution:
For finding the Median we have to build a table with cumulative frequency as,
Marks 0-20 20-40 40-60 60-80 80-100 Number of Students 5 7 9 4 5 Cumulative Frequency 0+5 = 5 5+7 = 12 12+9 = 21 21+4 = 25 25+5 = 30 n = ∑fi = 5+7+9+4+5 = 30(even)
n/2 = 30/2 = 15
Median Class = 40-60
Now using the formula,
Median = l + [(n/2 – cf) / f]×h
Comparing with the given data we get,
- l = 40
- n = 30
- f = 9
- h = 10
- cf = 21
Median = 20 + [(15 – 21)/6]×10
= 40 – 1/10
= 40 – 0.1
= 39.9
Thus, the median mark of the class test is 39.9
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