Before you understand What is Median ?
You must know:
What is Ascending Order ?
What is Descending Order ?
Definition
In a given set of observation, after arranging in ascending or descending order, the middle observation which divides the set of observation in two equal parts is referred to as Median .
In order words, Median refers to the value which lies in the middle of the set of data, which is arranged in ascending or descending order.
Steps to find Median where the numbers of integers are odd in a given set of observations or data
Step 1 - Arrange the given set of observations or data in ascending or descending order.
Step 2 - Find the middle value, which divides the given data in two equal parts.
Example 1 - Following data represents weight of 11 students in a class. Find Median.
35, 29, 37, 38, 41, 36, 42, 47, 39, 40, 48
Answer - Follow the steps as explain above :
Step 1 - Arrange the given set of observations or data in ascending order and we get;
29, 35, 36, 37, 38, 39, 40, 41, 42, 47, 48
Step 2 - Find the middle value, which divides the given data in two equal parts.
29, 35, 36, 37, 38, 39, 40, 41, 42, 47, 48
You can see value 39 is the middle of set of data and divides the given data in a two equal groups comprising 5 values each.
Hence, 39 is the Median of the data.
Example 2 : Following data represents score of 15 students in a science. Find Median
75, 80, 91, 76, 82, 93, 78, 83, 94, 84, 96, 79, 87, 89, 90
Answer - Follow the steps as explain above :
Step 1 - Arrange the given set of observations or data in descending order and we get;
96, 94, 93, 91, 89, 90, 87, 84, 83, 82, 80, 79, 78, 76, 75
Step 2 - Find the middle value, which divides the given data in two equal parts.
96, 94, 93, 91, 89, 90, 87, 84, 83, 82, 80, 79, 78, 76, 75
You can see value 84 is the middle of set of data and divides the given data in a two equal groups comprising 7 values each.
Step 3 - Hence , 84 is the Median of the data.
Steps to find Median where the numbers of integers are even in a given set of observations or data
Step 1 - Arrange the given set of observations or data in ascending or descending order.
Step 2 - select the middle 2 numbers from the given data set
Let's try some examples to find median on even data set of integers
Example 3 : Find median from the following set of even numbers
3 2, 5 7, 11, 13, 19, 19, 29, 23
Answer : The steps are :
Step 1 - Arrange the given set of observations or data in ascending order and we get;
2, 3, 5 7, 11, 13, 19, 19, 23, 29
Step 2 - Select the middle 2 numbers from the given data set i.e.
2, 3, 5 7, 11, 13 , 19, 19, 23, 29
So median is 12
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