Median Formula: The median is the middle of a group of numbers. It is a simple way to represent a lot of data with just one number. To find it, you put the numbers in order and pick the middle one. In this article, you will find the meaning of median with its definition, formula and calculation process with solved examples
Median Meaning: What is Median?
The median is like finding the middle number in a list of numbers. To find the median, just put the numbers in order and choose the middle number.
Median Definition
The median is a statistical measure that represents the middle value in a dataset when it is sorted in ascending or descending order. It is commonly used in various fields, including statistics, economics and data analysis.
Median Formula
Calculating the median depends on whether we have an even or odd number of values in our data set, so it's important to figure that out first.
How to Calculate Median For Odd Number of Observations
If you have n observations,
For odd number of observations, median = [(n+1)/2]th term
How to Calculate Median For Even Number of Observations
If you have n observations,
For even number of observations, median = [(n/2)th term + {(n/2) + 1}th term]/2
Solved Examples
Example 1: The age of the girls in the Science fair is listed as {42,40,50,75,35,58,30}. Find the median of the given set of numbers.
Solution:
Given set 42,40,50,75,35,58,30
Arranged set in ascending order 30,35,40,42,50,58,75
Here, the number of observations (n) = 7.
Median formula when 'n' is odd = {(n + 1)/2}th term]
Median = [(7 + 1)/2]th term = (8/2)th term = 4th term.
The 4th observation is 42.
The median of the set {30,35,40,42,50,58,75} is 42
Example 2: What is the median of the first 6 whole numbers.
Solution:
The first 6 whole numbers are 0, 1, 2, 3, 4, 5.
Number of observations (n) = 6.
Median = [(n/2) + 1]th term = 4th term
Therefore, median of the first 6 whole numbers is 3.
Example 3: The number of candies that Riya bought on each day of a week were: 1, 2, 2, 3, 4, 3, 3, 5. What is the median value of the number of candies she bought?
Solution:
The original set: 1, 2, 2, 3, 4, 3, 3, 5.
Arranged set: 1, 2, 2, 3, 3, 3, 4, 5.
Number of observations(n) = 8.
Since the number of observations is odd, median = [(n/2)th term + {(n/2) + 1}th term]/2
= (4th term + 5th term) / 2
= 3rd term
Thus, median = 2
Example 4: Number of vlogs posted each week by a YouTube channel in the month of December 2022 is 2, 1, 3, 3.
Solution:
The data arranged in increasing order is 1, 2, 3, 3.
Number of observations (n) = 4.
Median = [(n/2) + 1]th value = 3rd value
Therefore, median is 3.
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