Interquartile Range (IQR) Calculator
Compare Q1, Q2, Q3 and IQR under the TI-83/84/AP exclusive rule, Tukey’s inclusive hinges and Excel QUARTILE.INC interpolation. See the 1.5 × IQR fences, potential outliers and a live box plot.
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- Worked steps
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100% Local in Browser — Your Data Never Leaves This Tab
Comma, space, tab or newline separated. Paste an Excel column directly; blank lines and labels are ignored.
Try a sample
Paste a dataset to begin
The worked steps, table, box plot and summary update as you type. Nothing is sent anywhere.
How it works
- 1
Paste and split
The sorted data is split into halves. On an odd count, the exclusive convention removes the median before splitting; Tukey’s inclusive convention keeps it in both halves. The page shows all three answers rather than choosing one silently.
- 2
Compare the conventions
TI-83/84 and AP Statistics usually expect the exclusive method. Excel QUARTILE.INC and R type 7 use linear interpolation at position (n − 1)p, which can produce a Q1 that is not an observed value. The three cards label the difference.
- 3
Apply the fence
IQR = Q3 − Q1. Values below Q1 − 1.5·IQR or above Q3 + 1.5·IQR are potential outliers. The box plot marks them as dots; the fence card shows the exact arithmetic for the active convention.
More tools
- Median CalculatorPaste a dataset and get the median with the sorted list, the exact middle position or pair, and a box plot. Odd and even counts are handled separately, and the numbers never leave your browser.
- Mean CalculatorAdd a list of numbers and see the mean with the sum, the count and every substitution in Σx / n. The dataset stays in your browser and carries over to the median, SD, IQR and z-score pages.
- Standard Deviation CalculatorGet sample or population SD with a row-by-row deviation table, the definition formula and the computational Σx² − n·x̄² formula. Copy the APA result or switch to population variance without re-pasting the data.
- Average CalculatorFind the average of any list with the sum, count and substitution shown line by line. Also called an average finder; the page reports the arithmetic mean and compares it with the median so a skew does not fool you.
- Z-Score CalculatorTurn x, μ and σ into a z-score and a left-tail, right-tail or two-tailed probability, or standardize every value in your dataset at once. The standard normal curve fills the same area the table reports.
What it won't do
- There is no universal “correct” quartile convention. TI-83/84 and many AP rubrics use exclusive; Tukey’s hinges use inclusive; Excel QUARTILE.INC uses linear interpolation. Choose the one your course specifies and state it.
- The 1.5 × IQR rule is a screening heuristic, not a formal test. A point outside the fence is a potential outlier, not proof of a data error or a non-normal population.
- For n < 4 the half-splitting methods become ill-defined; the page falls back to linear quartiles and the convention rows may coincide.
- The box plot uses the active convention. Switching methods can move a point inside or outside the fence, which is exactly why the page keeps the comparison visible.
Questions
Why does Excel give a different IQR than my TI-84?
Excel QUARTILE.INC uses linear interpolation at position (n − 1)p, while TI-83/84 uses the exclusive median-of-halves method. On the nine-value sample 12, 15, 18, 20, 22, 25, 28, 31, 35, TI-84 gives Q1 = 16.5 and Q3 = 29.5; Excel gives Q1 = 18 and Q3 = 28. Both are defensible, but the course rubric picks one.
What is Tukey’s inclusive method?
Tukey’s hinges keep the median in both halves when n is odd. For the same nine values, Q1 becomes 18 and Q3 becomes 28. This is the inclusive convention shown as Method B; it often agrees with the linear result at these quartile positions but is defined differently.
How do you find outliers with the IQR rule?
Compute the fences Q1 − 1.5 × IQR and Q3 + 1.5 × IQR. Any value strictly below the lower fence or above the upper fence is a potential outlier. The With Outlier preset puts 98 far above a fence of about 50.5, so it is marked separately on the plot.
Is the IQR the same as the range?
No. Range is max − min and uses only two observations. IQR is Q3 − Q1 and covers the middle half of the data, so one extreme value cannot inflate it the way it inflates the range.
Which quartile method should I use for AP Statistics?
AP Statistics classrooms commonly teach the TI-83/84 exclusive method: for an odd n, do not include the median in either half. Follow your teacher’s rubric if it names a different convention, and show the method in your work.
Does the page draw the box plot from the selected method?
Yes. The box, whiskers, median line and outlier dots all use the active convention, and the fence text updates with it. The three comparison cards remain visible so you can see how the plot would move under another convention.