# How to find the Median of Odd Numbers?

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The median refers to the middlemost value in the given data set. It divides our data set into two equal parts with 50% of data values lying below and 50% of the values lying above the median. There are different formulas for calculating the median depending on whether the number of data values is odd or even.

### Formula to find Median of Odd Numbers:

We first arrange the data in either ascending or descending order. Let n denote the number of data values. If n is odd then the median of odd numbers can be found using the formula, \text{Median } =\left( \frac{n+1}{2}\right )^{th}\text{ term}.

#### Example 1:

Calculate the median for the following set of data: 3, 9, 7, 6, 5, 2, 8, 11, 9

Solution: We first arrange the data in ascending order as shown below: 2, 3, 5, 6, 7, 8, 9, 9, 11 Since we have 9 data values we have that n=9 is odd. Therefore we now use the above formula, \text{Median } =\left( \frac{n+1}{2}\right )^{th}\text{ term}.\text{Median } =\left( \frac{9+1}{2}\right )^{th}\text{ term}.\text{Median } =\left( \frac{10}{2}\right )^{th}\text{ term}.\text{Median } =5^{th}\text{ term} = 7.

#### Example 2:

Calculate the median for the following set of data: 7, 9, 6, 8, 12, 17, 13,

Solution: We first arrange the data in descending order as shown below: 17, 13, 12, 9, 8, 7, 6 Since we have 7 data values we have that n=7 is odd. Therefore we now use the above formula, \text{Median } =\left( \frac{n+1}{2}\right )^{th}\text{ term}.\text{Median } =\left( \frac{7+1}{2}\right )^{th}\text{ term}.\text{Median } =4^{th}\text{ term} = 9. We can verify that there are three data values lying above 9 and three data values lying below 9. Hence the median divides our data into two equal parts.

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