Quartile and Interquartile Range Calculator
Paste data to get the quartiles, IQR and five-number summary, see a box plot, and find outliers with the 1.5 × IQR rule.
Quartiles, IQR and outliers
Quartiles cut sorted data into four groups with equal counts. The interquartile range, Q3 − Q1, is the width of the middle 50% and is the natural measure of spread to pair with the median, because neither is thrown off by extreme values.
Tukey’s 1.5 × IQR rule flags points more than one and a half box-widths beyond the box. For normally distributed data only about 0.7% of values fall outside those fences, so a flagged point deserves a second look: a typing error, a different population, or a genuinely rare event.
Need a different cut-off, such as the 90th percentile? Use the percentile calculator.
Frequently asked questions
How do you find Q1 and Q3?
Sort the data and find the median. Q1 is the median of the lower half and Q3 is the median of the upper half. With an odd number of values, the overall median is left out of both halves. This is the method used by TI-84 calculators and most introductory textbooks.
Why does Excel give different quartiles?
Excel’s QUARTILE.INC and QUARTILE.EXC interpolate between ranks instead of splitting the data into halves. All three methods are legitimate, and they agree for large data sets. This page shows all three so you can match your course or software.
How do I find outliers with the IQR?
Compute IQR = Q3 − Q1. The lower fence is Q1 − 1.5 × IQR and the upper fence is Q3 + 1.5 × IQR. Any value outside the fences is flagged as a potential outlier. It is a screening rule from John Tukey, not a reason to delete data automatically.
What is the five-number summary?
Minimum, Q1, median, Q3 and maximum. It describes the centre, spread and range of a data set, and is exactly what a box plot draws.
How do I read a box plot?
The box spans Q1 to Q3, so it holds the middle half of the data. The line inside is the median. Whiskers reach to the most extreme values that are not outliers, and dots beyond them are outliers. A median off-centre in the box, or one whisker much longer than the other, suggests skew.