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Interquartile Range Calculator

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.

Calculate Interquartile Range

Enter your data values separated by commas, spaces, or line breaks.

Enter at least 4 numerical values. Decimal and negative numbers are supported.
Interquartile Range (IQR)
0
First Quartile (Q1) 0
Median (Q2) 0
Third Quartile (Q3) 0
Total Values 0

What Is the Interquartile Range?

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.

IQR = Q3 − Q1

How Does the Interquartile Range Calculator Work?

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.

  1. Enter all values from your data set.
  2. The calculator sorts the numbers in ascending order.
  3. The median of the complete data set is calculated as Q2.
  4. The lower half of the data is used to calculate Q1.
  5. The upper half of the data is used to calculate Q3.
  6. Q1 is subtracted from Q3 to find the Interquartile Range.

Interquartile Range Formula

The formula for calculating the Interquartile Range is:

IQR = Q3 − Q1

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.

Interquartile Range Example

Consider the following sorted data:

2, 4, 6, 8, 10, 12, 14, 16

The lower half is:

2, 4, 6, 8

The median of the lower half gives:

Q1 = (4 + 6) ÷ 2 = 5

The upper half is:

10, 12, 14, 16
Q3 = (12 + 14) ÷ 2 = 13
IQR = 13 − 5 = 8

Why Is the Interquartile Range Important?

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.

Lower Outlier Limit = Q1 − 1.5 × IQR
Upper Outlier Limit = Q3 + 1.5 × IQR

Interquartile Range vs Regular Range

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.

Frequently Asked Questions

The Interquartile Range is calculated using the formula IQR = Q3 − Q1. Q3 is the third quartile and Q1 is the first quartile.
The IQR measures the spread of the middle 50% of values in a data set.
No. Since Q3 is greater than or equal to Q1, the Interquartile Range is always zero or a positive number.
The IQR focuses on the middle half of the data, so extreme values have less influence on it than they do on the regular range.
Q1 represents the first quartile, Q2 represents the median, and Q3 represents the third quartile of a sorted data set.
Yes. This calculator supports positive numbers, negative numbers, whole numbers, and decimal values.