Interquartile Range Formula

• Q1 is the “middle” value in the first half of the rank-ordered data set.
• Q2 is the median value in the set.
• Q3 is the “middle” value in the second half of the rank-ordered data set.

 The formula for inter-quartile range is given below

\[\large IQR=Q_{3}-Q_{1}\]

Where,
IQR=Inter-quartile range
Q₁ = First quartile
Q₃ = Third quartile

Q₁ can also be found by using the following formula

\[\large Q_{1}=\left(\frac{n+1}{4}\right)^{th}term\]

Q₃ can also be found by using the following formula:

\[\large Q_{3}=\left(\frac{3(n+1)}{4}\right)^{th}term\]

In these cases, if the values are not whole number, we have to round them up to the nearest integer.

Q₂ can also be found by using the following formula:

Q₂ = Q₃ – Q₁

Which is equivalent to median.

Solved Examples

Question: Find the inter-quartile range for first ten odd numbers: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 ?

Solution:

Total number of terms n = 10.

Median =

Median =

Therefore, the set of data is divided into two parts: 1, 3, 5, 7, 9 and 11, 13, 15, 17, 19

Q₁ = Median of first part = 5
Q₃ = Median of second part = 15

Formula for inter-quartile range is given by: IQR = Q₃ – Q₁
IQR = 15 – 5 = 10