Calculate the Interquartile Range (IQR) of your data set instantly. Find the first quartile, median, third quartile, and understand how your middle 50% of data is distributed.
Enter your data values separated by commas, spaces, or line breaks.
The Interquartile Range, commonly called IQR, is a statistical measurement used to describe the spread of the middle 50% of values in a data set. It is calculated by subtracting the first quartile from the third quartile.
Unlike the regular range, which considers only the smallest and largest values, the interquartile range focuses on the central portion of the data. This makes it especially useful when a data set contains extreme values or outliers.
This calculator automatically sorts your numerical data from the smallest value to the largest value. It then calculates the median, first quartile, third quartile, and finally the Interquartile Range.
The formula for calculating the Interquartile Range is:
Where Q1 represents the first quartile and Q3 represents the third quartile. The IQR shows how widely the middle half of the data is spread.
Consider the following sorted data:
The lower half is:
The median of the lower half gives:
The upper half is:
The Interquartile Range is useful because it provides a reliable measurement of data spread without being heavily affected by extreme values. This makes it particularly useful for identifying the typical spread of a data set.
IQR is commonly used in statistics, education, scientific research, business analysis, finance, data science, and box plot analysis. It can also help identify potential outliers in a group of values.
The regular range measures the difference between the highest and lowest values in a data set. It is simple to calculate but can be strongly affected by extreme values.
The Interquartile Range focuses only on the middle 50% of the data. Because it ignores the most extreme values, it often provides a more useful measurement of spread when outliers are present.