Interquartile Range: Overview, Questions, Preparation

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Rachit Kumar SaxenaManager-Editorial

Updated on Aug 5, 2021 08:24 IST

Table of Contents

What is Interquartile Range?
Weightage of Interquartile Range in Classes 11 and 12
Illustrated Examples on Interquartile Range
FAQs on Interquartile Range

What is Interquartile Range?

The interquartile range (IQR) is defined as the smallest of all the measures of dispersion. It is calculated as the difference between the two extreme observations or results of the distribution. In statistical terms, the difference that the third and the first quartile have between them is defined by the interquartile range.

Formula for Interquartile Range

Interquartile range = Upper Quartile - Lower Quartile
= Q₃ - Q₁

Steps for Calculating the Interquartile Range

Start by arranging the given set of numbers in an ascending or descending order.
Next is, counting the given number of values, which, if turns odd, means the centre value is median or else obtain the mean values for two centre values, known as Q₂ value.
The given set of values can be divided into two halves from the above-obtained median, denoted as Q₁and Q₃.
Find one median value from Q₁ values.
Find one median value from Q₃values.
Now, subtract the derived median values of Q₁ and Q₃.
The resultant value after subtraction is the IQR.

Weightage of Interquartile Range in Classes 11 and 12

For Class 11 Economics, the interquartile range is taught under the chapter ‘Statistical Tools and Interpretation’, the total marks for which is 27. For Class 11 Mathematics, it is taught under the unit ‘Statistics and Probability,’ in respect of which, the total marks allocated is 12.

Illustrated Examples on Interquartile Range

1. Calculate the interquartile range value for the first ten prime numbers.

Solution.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29 are the first ten prime numbers, which are already in ascending order.

The number of values given = 10

And, since the number of values given is an even number, the median will be the mean of the values 11 and 13, which gives Q₂ = 12 (11+13)/2

The two parts, i.e. Q₁and Q₂ are
Q₁: 2, 3, 5, 7, 11
The given number of values in Q₁ = 5, which is an odd number. So, the centre value taken is 5.

Therefore, Q₁ = 5

Q₃ = 13, 17, 19, 23, 29
The given number of values in Q₃ = 5, which is an odd number. So, the centre value taken is 19
Therefore, Q₃ = 19

Now, by subtracting Q₁ and Q₃ (19-5), the resulting value is = 11
Hence, the Interquartile Range (IQR) = 11

2. Find the IOR for the below series:

65, 41, 48, 12, 58, 2, 53, 47, 66, 25, 54

Solution.

Ascending order of the above series = 2, 12, 25, 41, 47, 48, 53, 54, 58, 65, 66
Number of values given = 11. Therefore, Median = 48
So, Q₁ = 2, 12, 25, 41, 47 & Q₃ = 53, 54, 58, 65, 66
The center value for Q₁ = 25 and for Q₃ = 58
Therefore, interquartile range = Q₃ - Q₁
= 58-25
= 33.

FAQs on Interquartile Range

Q: Why is the interquartile range so important?

A: Finding the interquartile range is important because it is used to determine when a value is in outliners. IQR is significant in knowing the extent to which the entire data is spread.

Q: What are quartiles?

A: Quartiles are the partitional values that split the whole series into four (04) equal values or parts, making three (03) quartiles. The three quartiles are called first or lower quartile, the second quartile, and the third or upper quartile, which are denoted by Q ₁, Q ₂, and Q ₃ respectively.

Q: What is the relation between the median and the interquartile range?

A: In a given data, the middle value of the distribution is said to be the median. The interquartile range means the range of values that are found in the middle of the scores. By skewing a distribution and using the median instead of the mean to display a central tendency, the appropriate measure of variability that comes as the outcome is the interquartile range.

Q: What is the semi-interquartile range?

A: Quartile deviation or semi-interquartile range is half of the distance measured between the third quartile and the first quartile.
Quartile deviation = (Q ₃ - Q ₁)/2

Q: What is another name for interquartile range?

A: The interquartile range is also known as midspread.