Statistics
Quartile Calculator
Quartiles split sorted data into four equal parts, but textbooks, Excel, and TI calculators do not agree on where Q1 and Q3 sit.
Paste your data, pick a method, and mathcheck returns Q1, the median, Q3, and the IQR, shows every other method's answer for comparison, and draws a box plot with fences and outliers.
Any order; separate with commas, spaces, or new lines.
Median split matches most school textbooks and TI-84 calculators.
Try an example
Result
Quartiles Q1 | Q2 | Q3
—
- Q1
- —
- Q2 (median)
- —
- Q3
- —
- IQR
- —
- Five-number summary
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the quartile calculator solves
Quartiles split sorted data into four equal parts, but textbooks, Excel, and TI calculators do not agree on where Q1 and Q3 sit. Paste your data, pick a method, and mathcheck returns Q1, the median, Q3, and the IQR, shows every other method's answer for comparison, and draws a box plot with fences and outliers.
Formula
How to use it
- Paste the data in any order.
- Pick the quartile method that matches your course: median split for most textbooks and TI-84, inclusive for Excel QUARTILE.INC and R, exclusive for Excel QUARTILE.EXC and Minitab.
- Read Q1, Q2, Q3, and the IQR, then check the comparison rows to see whether another method would change the answer.
- Use the box plot to spot skew and outliers.
How to read the answer
Q1 marks the bottom quarter, Q2 the middle, Q3 the top quarter. A box that sits far from the center of the whiskers signals skew, and a long whisker on one side means a stretched tail. The IQR describes the spread of the middle half and is not affected by extreme values, which is why it anchors the 1.5 × IQR outlier fences.
Common mistakes and edge cases
- Forgetting to sort before splitting into halves.
- Including the median in both halves in one problem and excluding it in the next; pick one rule and state it.
- Expecting Excel and a TI-84 to agree; they use different interpolation rules and can differ by a full data step.
- Reading Q3 - Q1 as the range; the range is max - min.
Worked examples
Even count, median split
Quartiles Q1 | Q2 | Q3
36 | 40.5 | 43
Odd count, median excluded
Quartiles Q1 | Q2 | Q3
2.5 | 5 | 7.5
Odd count, Tukey hinges
Quartiles Q1 | Q2 | Q3
3 | 5 | 7
Inclusive (Excel QUARTILE.INC)
Quartiles Q1 | Q2 | Q3
2.75 | 4.5 | 6.25
Exclusive (Excel QUARTILE.EXC)
Quartiles Q1 | Q2 | Q3
2.25 | 4.5 | 6.75
Negative and decimal values with an outlier
Quartiles Q1 | Q2 | Q3
-0.25 | 1.75 | 2.75
Too little data
Quartiles Q1 | Q2 | Q3
Error
Frequently asked questions
How do I find Q1 and Q3 by hand?+
Sort the data and find the median. Q1 is the median of the values below the overall median, Q3 the median of the values above it. For an odd count most textbooks leave the middle value out of both halves.
Why does Excel give a different quartile than my textbook?+
Excel's QUARTILE.INC uses position 1 + p(n - 1) with interpolation, QUARTILE.EXC uses p(n + 1), and textbooks usually use the median-split rule. All are valid; they just interpolate differently, so state which one you used.
What is the interquartile range used for?+
IQR = Q3 - Q1 measures the spread of the middle 50% and defines the 1.5 × IQR outlier fences used in box plots. It ignores extreme values, unlike the range or standard deviation.
What are Tukey's hinges?+
Tukey's original box-plot quartiles: split at the median and, when n is odd, include the median in both halves. They match the median-split rule for even n.
How do I read a box plot?+
The box runs from Q1 to Q3 with a line at the median. Whiskers reach the most extreme values inside the fences, and dots beyond the whiskers are outliers. A longer side of the box or a longer whisker shows where the data is stretched out.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026