Interquartile Range Formula with Problem Solution & Solved Example

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The interquartile range in mathematics is a measure of middle value in the given data set. Whenever a range is measured, there is one beginning value and the ending value in the dataset with bulk values in between. It can be used to measure the spread i.e. average or the median when you want to test school performance or SAT scores etc.

In general, the interquartile range formula is the subtraction of first quartile value from the third quartile value as mentioned below –

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

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

Take an example where all datasets are arranged on a number line. If you wanted to calculate any particular value from the dataset that is centred at zero and stretching values infinitely either above zero or below zero in a series. Once you have the plotted the values on the number line, the smallest or the largest values in a dataset will set the set the boundaries for a particular interval space that contains all data points in a set.

Data sets could also be divided in percentages instead of quarters. There is an option to use calculator as well but we strongly recommend to understand the logic first so that you can use the calculator fruitfully.

The IQR concept is generally used to spread out the data points in a data set. The higher the IOQ value, the data points would spread out more in the same ratio around the mean. This is best to use with other measurements too like median, cluster tendency or more.