# How to find the interquartile range of a set of numbers

We will use the concept of median to find the interquartile range of a set of numbers.

## Answer: The interquartile range is found by the differences between the higher Quartile and Lower Quartile in a given set of data.

**Explanation :**

Let us consider a set of few numbers 1, 2, 3, 5, 7, 9, 12, 15, 16, 19, 20

Now, let's find the median of the above set of numbers.

To find the median first step is to write all the numbers in ascending order.

Formula to find the median of an odd number of terms is given by (n+1) / 2th term

= 6th term [ on substituting n as 11 ]

Hence the median of the above set of terms = 9 [ which is the 6th term from the set of given values ]

Now make two groups from the above set of numbers,

1) Smaller numbers than 9 (median) = ( 1, 2, 3, 5, 7)

2) Greater numbers than 9 (median) = (12, 15, 16, 19, 20)

Now finding the medians of the above 2 sets of numbers

Median of 1st group = 3

Median of 2nd group = 16

Interquartile range = Median of 2nd group - Median of 1st group = 16 - 3 = 13

### The interquartile range is found by the differences between the higher Quartile and Lower Quartile in a given set of data.