IQR Formula
The distance between the first quartile and the third quartile is called the interquartile range (IQR), and in this section, we will learn about the interquartile range formula. Before moving to the formula part, let us understand what the first quartile and third quartile mean. First Quartile  \(Q_1 \): It is the data point located between the median and the smallest number of the given data. It divides the data at the 25% mark. Third Quartile \(Q_3 \): It is the data point located midway between the median and the highest number of the given data. It divides the data at the 75% mark. Let's learn about the IQR formula with a few examples in the end.
What Is the IQR Formula?
IQR formula is mostly used for measuring the variability, which is based on segregating the data entries into quartiles. The formula for the interquartile range is as follows:
Interquatile range (IQR) Fomrula = \(Q_3  Q_1 \)
In the next section, we will be solving a few examples of the IQR formula and learn more about the concept.

Example 1: Jane finds the first quartile and the third quartile values of the data to be 43 and 71 respectively. Can you help Jane to find the interquartile range for this data?
Solution:
The known values are:
\(Q_1 = 43 \) and \(Q_3 = 71 \)
Interquartile range = \(Q_3  Q_1 = 71  43 = 28 \)
Answer: The interquartile range is 28

Example 2: Patrick wants to know the interquartile range of the set of the first 100 whole numbers. How can you help Patrick?
Solution:
Listing the first 100 natural numbers, we have 1, 2, 3, ..........98, 99, 100
Taking the first half of the data, 1, 2, 3,.......48, 49, 50 we can find the first quartile value.
First Quartile = \(Q_1 = \dfrac{25 + 26}{2} = \dfrac{51}{2} = 25.5 \)
Now taking the second half of the data, 51, 52,53, ....... 98, 99,100 we can find the third quartile value.
Third Quartile = \(Q_3 = \dfrac{75 + 76}{2} = \dfrac{151}{2} = 75.5 \)
Interquartile range = \(Q_3  Q_1 = 75.5  25.5 = 50 \)
Answer: The interquartile range is 50