Quartile and IQR Calculator

Quartiles divide a sorted data set into four equal groups. The first quartile (Q1) is the value below which the bottom 25% of the data falls; the second quartile (Q2) is the median, splitting the data exactly in half; and the third quartile (Q3) is the value below which 75% of the data falls. The interquartile range (IQR) is Q3 minus Q1 and represents the spread of the central 50% of your data. Because the IQR ignores the top and bottom quarters, it is not affected by extreme values and is often a better measure of spread than the full range when your data contain outliers. The IQR is also the basis of the Tukey fences, which identify potential outliers: the lower fence is Q1 minus 1.5 times the IQR and the upper fence is Q3 plus 1.5 times the IQR. Any value outside these fences is flagged as a potential outlier in many textbooks and statistical software packages. Quartiles are the foundation of the box-and-whisker plot, one of the most widely used tools for visualising data distributions. This calculator uses linear interpolation (the same approach as the percentile calculator) to handle data sets of any size. Enter your values as a comma-separated list of at least four numbers and you get Q1, Q2, Q3, IQR, lower fence, upper fence, and the count of data points. Data are sorted automatically. Useful for students learning descriptive statistics, analysts building box plots, and researchers checking the spread of a variable before further analysis.

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