Median Formula: Odd and Even Set of Numbers

Median Formula: The median is the value in a group that is in the middle. The median helps single data points represent a vast number of data points. The middle value of a group of integers can be calculated using the formula of median. How to find median? Let’s consider that the wickets taken by two bowlers in their last ten matches are: Bowler A: 2, 1, 0, 4, 2, 30, 20, 5, 0, 2 and Bowler B: 3, 0, 5, 1, 3, 2, 0, 3, 1, 6.

So, to calculate the median, we must start by arranging the data in ascending or descending order and applying the following rule. If the number of observations is even (in this case), then the median is: [(n/2)^th term + {(n/2)+1}^th term]/2 And, if the number of observations is odd, then the median is: {(n+1)/2}^th term.

Median Formula: What is Median in Maths?

One of the three metrics of central tendency is the median. When describing a data set, the data set’s centre position is determined. This is referred to as the central tendency measure. The mean, median, and mode are the three most popular central tendency metrics.

Formula of Median & Example for Odd Set of Numbers

Now that you are already aware of the formulas when n is odd and n is even let us explain the concept via example.

Example 1: Find the median for the following data set:
104, 58, 36, 102, 91, 101, 12.

• 1st Step: Arrange your data in ascending order (lowest value first and highest value last). Here the data set order will be 12, 36, 58, 91, 101, 102, 104.
• 2nd Step: Find the number that is placed exactly in the middle (there will be a single middle value): 12, 36, 58, 91, 101, 102, 104.

So, Median = 91 (lies in the middle as 3 numbers are before it and 3 numbers are after it).

The above can also be calculated by using the formula {(n+1)/2}^th term.

Total terms are 7 so n = 7. Placing the values in the formula we get:

Median = {(7+1)/2}^th term = {(8)/2}^th term = (4)^th term i.e., 91.

Median Formula Class 10 & Example for Even Set of Numbers

Here we will take a data set having an even number of values.
Example 2: Let us find the median for the given data set: 12, 54, 31, 100, 82, 103, 8, 59.

• – 1st Step: Arrange the data in descending order (highest value to lowest value). 103, 100, 82, 59, 54, 31, 12, 8.
• – 2nd Step: Find the two numbers that occur in the middle (since the value of n is even i.e. that data set has an even number of terms). 103, 100, 82, 59, 54, 31, 12, 8
• – 3rd Step: Now add the two numbers and then divide by 2, to get the average:

59 + 54 = 113 => 113/2 = 56.5.

The median is 56.5.

Now, calculating the same using formula [(n/2)^th term + {(n/2)+1}^th term]/2

Total terms = 8 so, n = 8. Now putting the value in formula:

Median = [(8/2)^th term + {(8/2)+1}^th]/2 => [(4)^th term + {4+1}^th]/2 = (59+54)/2

Median for even set of values = 113/2 = 56.5.

Mean Median Mode

Considering the exam point of view there are only a few incidents where only the median is asked. In a maximum number of scenarios, the questions will be framed in such a way that you have to find mean, median or mean, median, and mode as well. And the best way to explain this is by taking another example:

Example 3: Find the mean, median, and mode for 4,8,11,11,15,11,17.

So, Median = Middle Value = 11.

Mean = \(\frac{Sum\, of\, Observations} {Total\, Number\, of\, Observations}\) = (4+8+11+11+15+11+17)/5 = 77/7 = 11.

Mode = Value repeated most number of times = 11.

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FAQs on Median Formula Class 10

Here are some frequently asked questions on the formula of median that students look for:

Q. How to calculate median?
Ans. To calculate the median first check the number of data set. If the value of ‘n’ is odd use {(n+1)/2}^th term and for even ‘n’ value use [(n/2)^th term + {(n/2)+1}^th term]/2.

Q. What is the median of 77 and 84?
Ans. By using the formula for even value of ‘n’ [(2/2)^th term + {(2/2)+1}^th term]/2 => [77+84]/2 => 80.5.

Q. What is the median of 20 observations?
Ans. The median will be [10^th term + 11^th term ]/2.

Q4. How to find the median of an even set of numbers?
Ans. Follow the steps below to find the median of an even set of numbers:
(i) Arrange the data in descending order (highest value to lowest value).
(ii) Find the two numbers that occur in the middle.
(iii) Now add the two numbers and then divide by 2, to get the average.

Q5. How to find the median of an odd set of numbers?
Ans. Follow the steps below to find the median of an odd set of numbers:
(i) Arrange your data in ascending order (lowest value first and highest value last).
(ii) Find the number that is placed exactly in the middle (there will be a single middle value).

Want help with more formulas? Check out some more formulas given below.

Attempt 11th CBSE Exam Mock Tests

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