IQR Calculator
Calculate the interquartile range (IQR), lower and upper quartiles (Q1, Q3), median, and outliers. Free online IQR calculator with box plot and data distribution charts.
About This Calculator
The Interquartile Range (IQR) Calculator is a free online statistics tool that computes quartiles, median, interquartile range, and outliers for any dataset. The IQR measures the spread of the middle 50% of your data and is a robust measure of statistical dispersion that is resistant to outliers. Students, data analysts, and researchers use this calculator to quickly understand data distribution without manual computation.
To calculate the IQR, the calculator sorts your data in ascending order, then finds Q1 (the median of the lower half), Q2 (the overall median), and Q3 (the median of the upper half). The IQR is simply Q3 minus Q1. The calculator also applies the 1.5\u00d7IQR rule to identify potential outliers \u2014 values falling below Q1 \u2212 1.5\u00d7IQR or above Q3 + 1.5\u00d7IQR are flagged. The five-number summary (minimum, Q1, median, Q3, maximum) is displayed alongside the mean and standard deviation for a complete statistical profile.
How to interpret IQR results
A smaller IQR indicates that the middle half of your data is tightly clustered, while a larger IQR suggests greater variability. For example, test scores with an IQR of 10 points show more consistency than scores with an IQR of 30 points. Use the box plot chart to visualize the five-number summary, and the distribution chart to see how values are spread across bins.
Regional Notes
IQR is a universal statistical concept used identically in India, the US, the UK, and worldwide. The 1.5\u00d7IQR outlier rule is the standard method taught in statistics courses globally. Whether you are analyzing exam scores in Mumbai, income data in New York, or survey results in London, the IQR provides a consistent and reliable measure of data spread.
Frequently Asked Questions
What is interquartile range (IQR)?
The interquartile range (IQR) measures the spread of the middle 50% of a dataset. It is calculated as Q3 \u2212 Q1, where Q1 is the first quartile (25th percentile) and Q3 is the third quartile (75th percentile). The IQR is resistant to outliers, making it a robust measure of statistical dispersion.
How do you calculate Q1 and Q3?
To find Q1 (lower quartile), take the median of the lower half of the sorted dataset. To find Q3 (upper quartile), take the median of the upper half. When the dataset has an odd number of values, the median is included in both halves. When even, the dataset is split evenly.
What is the formula for IQR?
The IQR formula is: IQR = Q3 \u2212 Q1. For example, with dataset [3, 5, 7, 8, 9, 11, 15], Q1 = 5, Q3 = 11, so IQR = 11 \u2212 5 = 6. This means the middle 50% of values span a range of 6.
How is IQR used to detect outliers?
Outliers are detected using the 1.5\u00d7IQR rule. Any value below Q1 \u2212 1.5\u00d7IQR or above Q3 + 1.5\u00d7IQR is considered an outlier. For instance, if Q1 = 10, Q3 = 20, IQR = 10, values below \u22125 or above 35 are outliers.
What is the five-number summary?
The five-number summary consists of: minimum, Q1 (lower quartile), median (Q2), Q3 (upper quartile), and maximum. Together with the IQR, it provides a complete picture of data distribution and is the basis for box plots.
When should I use IQR instead of standard deviation?
Use IQR when your data has outliers or is skewed, as IQR is resistant to extreme values. Standard deviation is more appropriate for symmetrically distributed data without outliers. The IQR is commonly used in box plots and for identifying outliers.
Can IQR be negative?
The interquartile range is always non-negative. Since Q3 is always greater than or equal to Q1, the IQR (Q3 \u2212 Q1) is zero or positive. An IQR of zero means all values in the middle 50% are identical.