An interquartile range calculator should do more than subtract two hidden quartiles. Paste your data set and this tool sorts the values, shows Q1, the median, Q3, IQR, and the 1.5 x IQR outlier fences. The important choice is visible: the default uses the common classroom median-of-halves method, and you can switch to an inclusive-halves or interpolated percentile method when your textbook, spreadsheet, or statistics package expects it.
Find the first quartile and third quartile using the selected method, then subtract Q1 from Q3.
IQR = Q3 - Q1
Sort the data, split it around the median, then take the median of each half. The default excludes the center value when n is odd; the inclusive method reuses it in both halves.
Q1 = median(lower half); Q3 = median(upper half)
For p = 0.25 or p = 0.75, locate the fractional rank h in the sorted data and linearly interpolate between neighboring values.
h = 1 + (n - 1) * p
Values outside the inner fences are flagged as possible outliers; the calculator reports them without removing them.
Lower fence = Q1 - 1.5 x IQR; Upper fence = Q3 + 1.5 x IQR
The calculator first parses the numbers you paste, accepts commas, spaces, semicolons, tabs, line breaks, and simple fractions, then sorts the values from smallest to largest. The selected quartile method determines Q1 and Q3. The default method excludes the overall median from the two halves when the data count is odd. The inclusive method includes that median in both halves. The interpolated method uses the type-7 percentile formula commonly associated with software quantiles. After Q1 and Q3 are known, IQR is Q3 - Q1. The calculator then computes inner outlier fences at Q1 - 1.5 x IQR and Q3 + 1.5 x IQR and lists any values outside those fences without deleting them from the data.
DataForSEO People Also Ask example captured 2026-06-08
Data set: 4, 7, 7, 3, 5, 2, 6, 7, 9. Sort it to get 2, 3, 4, 5, 6, 7, 7, 7, 9. With the default exclude-center method, the median is 6, the lower half is 2, 3, 4, 5, and the upper half is 7, 7, 7, 9. Q1 is (3 + 4) / 2 = 3.5; Q3 is (7 + 7) / 2 = 7; IQR is 7 - 3.5 = 3.5.
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For 1, 2, 3, 4, 5, 6, 7, 8, the exclude-center median-of-halves method gives Q1 2.5, Q3 6.5, and IQR 4. The interpolated type-7 method gives Q1 2.75, Q3 6.25, and IQR 3.5. Neither is a typo; they are different quartile definitions.
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For 10, 12, 13, 14, 15, 16, 17, 18, 100, the default method gives Q1 12.5, Q3 17.5, and IQR 5. The inner fences are 12.5 - 7.5 = 5 and 17.5 + 7.5 = 25. The value 100 is above the upper fence, so the calculator flags it as a possible outlier.
Use this calculator when you are making a box plot, checking homework, summarizing a skewed data set, or screening for possible outliers before a report. IQR is useful when the middle spread matters more than the full min-to-max range, because one unusually high or low value does not dominate the result. If you need to match Excel, R, or a class handout exactly, pick the quartile method first and then compare the sorted values shown in the result.
Different tools use different definitions of Q1 and Q3. Many classroom examples split the sorted data into lower and upper halves and then take each half median. Some textbooks exclude the center value when the data count is odd; others include it in both halves. Software often uses interpolated percentiles. That is why two correct calculators can return different Q1, Q3, and IQR values for the same small data set. The safest workflow is to choose the method first, then check the sorted data and quartiles before submitting an answer.
The 1.5 x IQR fences are screening boundaries, not a deletion rule. A value below Q1 - 1.5 x IQR or above Q3 + 1.5 x IQR is far from the middle half of the data and deserves review. It might be a typo, a rare event, or a real observation from a skewed distribution. The calculator lists those values so you can investigate them before deciding whether to keep, correct, or explain them.
Start with the sorted-data preview. If a number looks missing, duplicated, or entered with the wrong sign, fix the input before trusting the quartiles. Next, confirm the quartile method. Homework pages usually expect the method taught in class; spreadsheet or statistics workflows may expect an interpolated percentile. Finally, remember that IQR summarizes only the middle half of the data. It is stable around extremes, but it does not describe the full range or every shape detail.
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