Calculating Interquartile Range

Calculating interquartile range is referred as a measure of variability, spread or dispersion, H-spread. It is the difference sandwiched between the 75th percentile (often called Q3 or third quartile) and the 25th percentile (often-called Q1 or first quartile). The primary step is to find the interquartile range is to arrange the given set of numbers in ascending order. The standard formula to find the interquartile range is given as

Interquartile ranges = Quart3 – Quart1.    ----- Standard formula

Whereas Q1 = first quartile.

Q3 = third quartile.

Example Problems for calculating interquartile range:

Ex : Determine the interquartile range of following set of numbers

34, 15, 8, 26, 22, 9, 19

Sol :  The following are the steps to find the interquartile range of a set of numbers.

Step 1:  Arranging of numbers

The initial step is to modify the given data in order, from smallest to biggest.

9, 8, 15, 19, 22, 26, 34

Step 2:    Calculating 1st quartile Q1.

The next step is to find the lower median (1st quartile Q!).

This is the middle of the lower three numbers.

1st quartile Q1 is 8.

Step 3:    Calculating 3rd quartile Q3.

Now find the upper median (The 3rd quartile Q2).

This is the middle of the upper three numbers.

The 3rd quartile Q3 is 26.

Step 4:     Calculating interquartile range.

The formula used to find the interquartile range is

Interquartile range = Q3 – Q1.

Q1 = first quartile.

Q3 = third quartile.

Here

Q1 the first quartile = 8

Q3 the third quartile = 26

Interquartile range = Q3 – Q1. ----- Standard formula

Plug in the Q1 and Q3 values in the standard formula Q3 – Q1.

Interquartile range = 26 – 8.

Interquartile ranges = 18.

Practice Problems for calculating interquartile:

Pro 1:  Find the interquartile range of following set of numbers

42, 81,56,21,63,12,5

Ans : Interquartile range = 51.

I am planning to write more post on substitution method examples and sample question papers for class 10 cbse. Keep checking my blog.

Pro 2:  Find the interquartile range of following set of numbers

56, 23, 14, 25, 86, 45, 63, 15, 49, 18, 16

Ans:   Interquartile range = 40.

Pro 3:   Find the interquartile range of following set of numbers

12, 8, 5, 22, 15, 45, 2

Ans :   Interquartile range = 17