# Median | Procedure | Median Formulas | Example

It is the numeric value that separates the higher digit values from the lower digit values. It is represented by $large dpi{100} bg_white bar{x}$. The median has some limitations. Median can only be defined for dimensional data and it is not dependent on any metric distance.

## Procedure For Finding Median

If the given data contain a finite number of values then first arrange the values in ascending order. Now after arranging pick up the single middle value which will be the median value. If the data contain an odd number of values then there will be only one single middle value & that will be the median of that data. But in case of an even number of values pick up two middle values and took the mean of these two values. This will give you the median value. This is also named as mean of the two middle values.

### Formulas For Median

• If “n” value is an odd number

$large dpi{100} bg_white {color{Blue} bar{x}}= left ( frac{n+1}{2} right )^{th} Ordered Value$

Where n is the total number of values a sample contain.

• If “n” value is an even number

$large dpi{100} bg_white bar{x}= left ( frac{n}{2} right )^{th} + left ( frac{n}{2}+1 right )^{th}mathbf{Ordered Value}$

The average of the two middle values

### Example For Median

#### Statement

Students of grade VI scores in maths paper are;

96, 88, 92, 83, 84, 72, 69, 100, 89, 99, 76, 86, 87

#### Requirement

• Find the median by using formulas.

#### Solution

##### Step I: Arrange the given data in ascending order

69, 72, 76, 83, 84, 86, 87, 88, 89, 92, 96, 99, 100

##### Step II: Find the value of “n” either odd or even.

n = 13  n is an odd number

##### Step III: Select median formula and evaluate the median.

As “n” is odd so we will use the first formula

$large dpi{100} bg_white {color{Blue} bar{x}}= left ( frac{n+1}{2} right )^{th} Ordered Value$