There are various measures of central tendency. One of them is the median. It can be defined as the middlemost value of the data. For example, if the observation is: 1, 2, 3, 4, 5. The median for the given data is 3. There are two mathematical formulas given to calculate the median of a given data. It is provided for odd and even sets of numbers. The formula for the odd set of numbers is n + ½ th term where ‘n’ is the number of observations. Similarly, the formula provided for the even set of numbers is, n/2th term + n/2 + 1th term / 2 where ‘n’ is the number of observations.

The median formula helps to get an appropriate value that represents a large set of values with the help of a single unit value. For the odd set of numbers, the median can be defined as the middlemost value of the observation. Similarly, for the even set of numbers, the median is considered as the average of the two middle values. In this article, we shall cover some basic topics regarding the median formula such as steps of doing it, calculations based on the odd, and even sets of numbers.

Table of Contents

## Calculation Based on the Odd set of numbers

The mathematical formula to calculate the median for the odd set of numbers is n + 1/2th observation where ‘n’ is denoted as the number of observations. Let us try to solve some examples related to the median formula for the odd set of numbers. Some of them are listed below.

**Example 1:** Calculate the median of the first five odd numbers?

**Solution:** Given that,

To calculate the median for the first five odd numbers,

First five odd numbers = 1, 3, 5, 7, 9. (arranged in ascending order).

For the odd set of numbers, formula = n + ½ th observation.

The total number of observations = 5.

Thus, 5 + ½ th observation = 6/2 th observation.

6/2 th observation = 3rd observation = 5.

Therefore, the median of the first five odd numbers is equivalent to 5.

**Example 2:** Calculate the median of the first seven even numbers?

**Solution:** Given that,

To calculate the median for the first seven even numbers,

First five odd numbers = 2, 4, 6, 8, 10, 12, 14. (arranged in ascending order).

For the odd set of numbers, formula = n + ½ th observation.

The total number of observations = 7.

Thus, 7 + ½ th observation = 8/2 th observation.

8/2 th observation = 4th observation = 8.

Therefore, the median of the first seven even numbers is equivalent to 8.

## Calculation Based for the Even Set of numbers

The mathematical formula to calculate the median for the even set of numbers is given as, n/2th term + n/2 + 1th term / 2 where ‘n’ is the number of observations. The median of the even set of numbers is written as the average of the two middle values. Some of the examples are listed below.

**Example 1:** Calculate the median for the even sets of numbers if the observation is: 1, 3, 2, 6, 8, and 9.

**Solution:** Given that,

Observation = 1, 3, 2, 6, 8, and 9.

Arranging in ascending order = 1, 2, 3, 6, 8 and 9.

Using the formula to calculate the median for the even set of numbers = n/2th term + n/2 + 1th term / 2.

6/2 th observation + 6/2 + 1th term / 2 = 3rd observation + 3 + 1th term / 2.

3rd observation + 3 + 1th term / 2 = 3rd observation + 4th term / 2 .

3 + 6 / 2 = 4.5

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