What is Median? – Median Meaning
The value of the middlemost observation, which is obtained by arranging the data in ascending or descending order, is referred to as the median of the data or we can also say that Median is a measure of central tendency which gives the value of the middlemost observation in a sorted list of data.
Again it also depends on whether we have even numbers of data or odd numbers of data.
Example:
Let’s take some ungrouped data i.e. 4, 4, 6, 3, 2, and we need to find the Median for these data. First of all we will arranges these data in ascending or descending order, and then we have to check whether we have an even number of data or an odd number of data. Depends of that we can figure out the median.
Step1: Arrange the data in ascending/descending order:
2, 3, 4, 4, 6
Step2: Count the number of data. Here, we have 5 observations that mean we have an odd number of data, and hence we will have one middle value.
Thus,
Median = middle value that is 4 here
Example:
Let’s take some ungrouped data set i.e. 1, 3, 2, 4, 5, 9, 8, 6, and we need to find the median of these data. Again, first of all we need to arrange the data in ascending or descending order and we need to check the number of data that are present in this given data set.
Step1: Arrange the given set of data in ascending/descending order:
1, 2, 3, 4, 5, 6, 8, 9
Step 2: Count the data. Here, we have 8 numbers of data, which is an even number. Hence here we will have two middle values:
1, 2, 3, 4, 5, 6, 8, 9
Step 3: To calculate the median in this case we need to take the average of these two middle values.
Hence, Median =
Let’s generalize the median of ungrouped data with the help of the following formulae:
Case 1: If n is odd, then the median formula is:
, Where,n is the number of observations
Case 2: If n is even, then the median formula is:
, Where,n is the number of observations
Median formula for grouped data
In case of Grouped data:
Median of Grouped Data formulae:
Step 1: Construct the cumulative frequency distribution.
Step 2: Decide the class that contains the median.
Step 3: Find the median using the following formula.
Where, l = Lower limit of median class.
n= Number of observations.
F = Cumulative frequency of class preceding the media class.
f = Frequency of mediumclass
h = Class size
Example: Based on the grouped data below, find the median.
Time to travel to workplace (Minute) 
Frequency(f) 
1 – 10  8 
11 – 20  14 
21 – 30  12 
31 – 40  9 
41 – 50  7 
Solution:
Step 1 – Construct the cumulative frequency distribution.
Thus, 25 people take less than 24 minutes to travel to work and another 25 people take more than 24 minutes to travel to work.
Example:
From the following distribution, find the median marks:
Classes  010  1020  2030  4050  4050 
Frequency  2  12  22  8  6 
To find the median, we need to calculate the cumulative frequencies.
Solution:
Calculation table is as follows:
Classes  Number of students  Cumulative frequency 
010  2  2 
1020  12  2 + 12 = 14 
2030  22  14 + 22 = 36 
3040  8  36 + 8 = 44 
4050  6  44 + 6 = 50 
n = 50
Then n/2 = 50/2 = 25
Hence, Median Class: 20−30
From this median class,
l = 20, f = 22, c = 14, h = 10
By using Median formula:
Assessments:
1 ) Find the median of the following data :
2, 4, 1, 9, 8, 6
2) During the summer vacations, Ram’s family drove through 7 states. The
Gasoline prices differ from state to state. Find the median of gasoline cost.
1.79, 1.61, 2.09, 1.84, 1.96, 2.11, 1.75
3) If the median of the distribution given below is 28.5, find the values of x and y.
Class interval  Frequency 
0 – 10  5 
10 – 20  x 
20 – 30  20 
30 – 40  15 
40 – 50  y 
50 – 60  5 
Total  60

4) The length of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table:
Length  Number of leaves 
118 – 126  3 
127 – 135  5 
163 – 144  9 
145 – 153  12 
154 – 162  5 
163 – 171  4 
172 – 180  2 
Some Important FAQs
 Explain Median with an Example.
A median is the middle value of a given list of observations when arranged in an order.
For instance,
A list of observations, we have
33, 66, 88, 22, 11
Now, arrange these values in ascending order,
We have
11,22,33,66, 88, if we observe here, total numbers of data we have 5, it means here there will be one middle value, hence the median will be the middle value, which is 33.
2. Explain the Median if we have two middle values (The number of data is even).
In this case we are required to apply the formula of median for even number of observations.
Thus,
For instance,
Median of 5, 15, 20, and 25
3. How to calculate the median of 10 numbers of observations?
For the 10 number observations,
4. Explain the median of odd numbers of observations.
For the odd number of observations,
Where,
n is the number of observations.
5. Explain the difference between mean and median.
Median is referred to as the middle value of an ordered list of values.
Mean is the ratio of the sum of a list of values and number of values, order of values is not considered.
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