Interquartile Range Calculator

How it works

Quartiles split a sorted data set into four equal-sized groups. Q1 (the lower quartile) marks the boundary of the bottom quarter of values, Q3 (the upper quartile) marks the boundary of the top quarter, and the interquartile range (IQR) is the distance between them:

IQR = Q3 − Q1

Because the IQR only covers the middle 50% of the data, it ignores the most extreme values at each end — which makes it a much more reliable measure of spread than the plain range (max − min) whenever your data contains unusually high or low values.

This calculator finds Q1 and Q3 using the median-of-halves method, the version most commonly taught in Australian high school maths classes:

1. Sort all the values from lowest to highest.
2. Find the position of the overall median.
3. If there’s an odd number of values, exclude that middle value entirely, then split the rest evenly into a lower half and an upper half. If there’s an even number of values, the data already splits cleanly down the middle, so nothing needs to be excluded.
4. Q1 is the median of the lower half. Q3 is the median of the upper half — using the same middle-value (or average-of-the-two-middle-values) rule as a standard median.

This is the exclusive method — the overall median is deliberately left out of both halves when the count is odd, rather than being included in one of them. It’s worth knowing that not every calculator does this the same way: some tools use an interpolation-based method instead, which estimates Q1 and Q3 at fractional positions along the sorted list rather than picking clean sub-medians. Both are legitimate statistical conventions, but they can give marginally different Q1 and Q3 values for the exact same data, so it’s normal for two “correct” IQR calculators to disagree slightly at the second decimal place.

Once Q1 and Q3 are known, this calculator also shows the outlier fence — the range outside which a value is conventionally flagged as a possible outlier, using Tukey’s widely-used 1.5×IQR rule:

Lower fence = Q1 − 1.5 × IQR
Upper fence = Q3 + 1.5 × IQR

A value doesn’t have to be wrong just because it sits outside the fence, but it’s a useful, consistent signal for “this point is unusually far from the rest of the group” worth a second look. See Khan Academy’s guide to the interquartile range for more on how IQR fits alongside the median and box-and-whisker plots.

Worked example

Liam is a real estate agent reviewing how much houses sold for on Jacaranda Street in Toowoomba, Queensland, over the past year. Nine houses changed hands, selling for (in $’000s):

465, 420, 610, 480, 525, 455, 510, 560, 495

Sorted from lowest to highest:

420, 455, 465, 480, 495, 510, 525, 560, 610

There are 9 values — an odd number — so the middle value, $495k (the 5th value), is the overall median and is excluded from both halves:

• Lower half: 420, 455, 465, 480
• Upper half: 510, 525, 560, 610

Each half has 4 values (even), so its median is the average of the two middle numbers:

• Q1 = (455 + 465) ÷ 2 = $460k
• Q3 = (525 + 560) ÷ 2 = $542.5k
• IQR = 542.5 − 460 = $82.5k

The outlier fence is Q1 − 1.5×IQR to Q3 + 1.5×IQR, or $460k − $123.75k to $542.5k + $123.75k — $336.25k to $666.25k. Every sale on Jacaranda Street this year falls comfortably inside that range, so Liam can tell his vendors the street had a consistent year: no sale was unusually cheap or unusually expensive next to its neighbours.

	Value ($’000s)
Q1 (lower quartile)	460
Median (excluded from Q1/Q3)	495
Q3 (upper quartile)	542.5
IQR	82.5
Outlier fence	336.25 – 666.25