Interquartile Range (IQR) Calculator

The IQR is a measure of statistical dispersion equal to Q3 minus Q1 — that is, the range of the middle 50% of your data. It tells you how spread out the central portion of your data set is, ignoring the lowest 25% and highest 25% of values. Because it ignores extreme values, the IQR is considered a robust measure of spread.

The regular range is simply the maximum minus the minimum, making it highly sensitive to outliers. The IQR instead measures the spread of the middle half of the data (Q3 − Q1), so a single extreme value cannot distort it. This makes IQR far more reliable when your data may contain outliers.

The standard method is the 1.5×IQR rule: calculate the lower fence as Q1 − 1.5×IQR and the upper fence as Q3 + 1.5×IQR. Any data point below the lower fence or above the upper fence is considered a mild outlier. For extreme outliers, use a multiplier of 3 instead of 1.5.

The Inclusive (Type-7) method interpolates between data points and is used by most statistical software including R, Python, and Excel's QUARTILE function. The Exclusive method excludes the median when splitting the data set and matches Excel's QUARTILE.EXC function. Tukey's Hinges uses the median to split the data into two halves and calculates Q1 and Q3 as the medians of those halves — this is the method used in box-and-whisker plots.

It depends on your data. Standard deviation considers every value and works best for normally distributed data without extreme outliers. IQR is more robust — it is unaffected by outliers or skewed distributions — making it the preferred measure when data is skewed or contains extreme values. For symmetric, roughly normal data, both measures are appropriate.

No — this calculator sorts your data automatically. You can paste numbers in any order, separated by commas, spaces, or new lines, and the calculator will handle the ordering before computing quartiles and the IQR.

The five-number summary is a concise description of a data set consisting of: Minimum, Q1 (25th percentile), Q2/Median (50th percentile), Q3 (75th percentile), and Maximum. Together with the IQR, these five values give a complete picture of your data's distribution and are the basis of box-and-whisker plots.

Use IQR when your data is skewed, contains outliers, or is measured on an ordinal scale. It is particularly useful in exploratory data analysis, income or salary data, test score distributions, and any situation where a few extreme values might mislead a mean-based analysis. For symmetric, well-behaved data, standard deviation is equally valid.