Quartile and Outlier Calculator
Paste a list of numbers and get the five number summary: the minimum, Q1, the median, Q3 and the maximum, plus the interquartile range, the outlier fences and a box plot. Choose from four quartile methods, because textbooks and spreadsheets do not agree. Everything runs in your browser.
Position (n - 1) x p + 1; same as R type 7 and most spreadsheets and Python NumPy.
9 to 17
3 outliers: -20, 18, 40. Extreme (beyond 3 x IQR): -20, 40
Whiskers run from 10 to 15. The mean is 12.461538 from 13 values.
The quartiles split sorted data into four parts: Q1 has a quarter of the values below it, the median is the middle, and Q3 has a quarter above it. The interquartile range, Q3 minus Q1, measures the spread of the middle half. A value more than 1.5 times the IQR below Q1 or above Q3 is usually called an outlier, and beyond 3 times the IQR an extreme outlier. There is no single agreed way to find a quartile: spreadsheets interpolate between values, while textbooks often take the median of each half, so the same data can give slightly different answers, which is why the method is a choice here. Everything is worked out in your browser and nothing is uploaded.
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Math & MoneyAbout the Quartile and Outlier Calculator
Quartiles split sorted data into four equal parts. Q1 has a quarter of the values below it, the median has half, and Q3 has three quarters. The interquartile range, IQR = Q3 minus Q1, is the spread of the middle half of the data. A common rule marks a value as an outlier when it is below Q1 minus 1.5 x IQR or above Q3 plus 1.5 x IQR, and as an extreme outlier beyond 3 x IQR. The box plot whiskers run to the smallest and largest values that are not outliers. There is no single definition of a quartile. The inclusive method, Excel QUARTILE.INC and R type 7, uses position (n - 1) x p + 1 and interpolates between values. The exclusive method, Excel QUARTILE.EXC and R type 6, uses position (n + 1) x p. The classroom method takes the median of the lower and upper halves and leaves the middle value out when the count is odd, and Tukey's hinges keep the middle value in both halves. For the numbers 1 to 9 they give Q1 and Q3 of 3 and 7 (inclusive), 2.5 and 7.5 (exclusive and halves) and 3 and 7 (Tukey). For 1 to 8 they give 2.75 and 6.25, 2.25 and 6.75, and 2.5 and 6.5. State which method you used when you report quartiles. Nothing is uploaded.
How do I find the quartiles of a data set?▾
Sort the numbers. The median is the middle value. With the halves method, Q1 is the median of the lower half and Q3 the median of the upper half. Spreadsheets interpolate instead, so results can differ slightly.
What is the interquartile range?▾
The IQR is Q3 minus Q1, the width of the range that holds the middle half of the data. It is not affected by extreme values, which makes it a robust measure of spread.
How are outliers found with the IQR?▾
A value is an outlier if it is below Q1 minus 1.5 x IQR or above Q3 plus 1.5 x IQR. These limits are called fences. Values beyond 3 x IQR are often called extreme outliers.
Why does Excel give different quartiles from my textbook?▾
Several definitions are in use. Excel QUARTILE.INC interpolates between values, QUARTILE.EXC uses a different position, and many textbooks use the median of each half. Pick the method your course or software expects.
Is my data uploaded?▾
No. The calculation runs in your browser and the numbers you enter are not sent anywhere.