Quartiles split a sorted dataset into four equal parts, and the interquartile range between them is one of the most reliable ways to describe how spread out your data is - especially when a few extreme values could otherwise distort the picture. This calculator computes Q1, Q2 (the median), and Q3 using either of the two standard median-split conventions, then uses the interquartile range to flag statistical outliers automatically.
How quartiles and IQR are calculated
Sort the observations. Q2 is the median. Q1 and Q3 are the medians of the lower and upper halves. The exclusive-halves convention excludes the overall median when n is odd; the inclusive-halves convention includes it in both halves. For even n, these two conventions agree. With tied observations, they can also agree for odd n.
These names describe the implemented median-split rules. Other quartile conventions, including interpolated percentiles, can give different results. State the selected convention with your result. IQR = Q3−Q1 describes the spread between the first and third quartiles.
Reading the outlier fences and box plot
Tukey's 1.5xIQR rule flags any value below Q1 minus 1.5 times the IQR, or above Q3 plus 1.5 times the IQR, as a potential outlier. This threshold is a widely used convention, not a hard mathematical law - it was chosen because, for roughly normal data, it flags only about 0.7% of values as outliers, a useful balance between over- and under-flagging.
The box plot on the IQR & Outliers tab visualizes all of this at once: the box spans Q1 to Q3, the line inside it marks the median, the whiskers extend to the most extreme values that are still inside the fences, the dashed lines mark the fences themselves, and any points beyond them are drawn as dots. A dataset with no outliers will show whiskers reaching all the way to its minimum and maximum.
When the two median methods matter
The Inclusive and Exclusive methods only produce different Q1/Q3 values when the dataset has an odd number of entries - for even-count datasets, they are mathematically identical every time. If your dataset has an odd count and you need to match a specific textbook, statistical software package, or exam answer key, check which convention that source uses; Excel's QUARTILE.INC/PERCENTILE.INC functions use a third convention entirely (linear interpolation), which can differ from both methods here for small datasets. The compare table on the Quartiles tab shows both results side by side so you can see exactly how much they diverge for your data.