Quartile Calculator

Quartiles divide an ordered data set into four sections. The first quartile, Q1, marks the point below which roughly one quarter of observations lie. The second quartile, Q2, is the median and splits the data in half. The third quartile, Q3, marks the point below which roughly three quarters of observations lie. Together with the minimum and maximum, these values form the five-number summary used in box plots and exploratory statistics. This calculator first sorts every entered number from smallest to largest. It finds the median of the full list, then finds Q1 from the lower half and Q3 from the upper half. When the list contains an odd number of observations, the central median is excluded from both halves. When a half has an even number of values, its quartile is the average of the two central values. This median-of-halves convention is widely taught, although software packages can use other percentile interpolation rules. The interquartile range, or IQR, equals Q3 minus Q1. It measures the spread of the middle 50 percent of observations and is resistant to extreme values. That resistance makes the IQR useful for skewed distributions, income data, response times, and other measurements where one unusually large or small observation can distort the ordinary range or standard deviation. A small IQR indicates a tightly clustered middle half; a large IQR indicates greater dispersion. A common outlier screen uses fences at Q1 minus 1.5 times the IQR and Q3 plus 1.5 times the IQR. Values outside those fences deserve investigation, but they are not automatically mistakes. They may be valid rare observations, signs of a heavy-tailed distribution, or data-entry errors. The scientific and operational context should determine how they are handled. Quartiles are especially useful for comparing groups because they summarize location and spread without assuming a normal distribution. Report the method used whenever exact quartile values matter, since different conventions can disagree on small samples. This tool displays the sorted sequence so you can verify the ordering and understand exactly how the summary was formed. Decimal values and negative numbers are supported, and repeated observations remain in the calculation because frequency is part of the distribution.