Quartile calculator: find Q1, Q2, Q3 and the interquartile range for any data set with the quartiles formula shown. Free, private, runs in your browser.
Q1 is the median of the lower half, Q3 the median of the upper half. IQR = Q3 − Q1.
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Worked example: six numbers, step by step
Take the dataset 4, 8, 15, 16, 23, 42 (n = 6). It is already sorted, so no reordering is needed. The tool splits it by floor(n/2) and ceil(n/2): the lower half is the first 3 values (4, 8, 15) and the upper half is the last 3 values (16, 23, 42). With an even count, no single middle value belongs to either half, so nothing is dropped.
Each half has an odd length (3), so its median is the middle value directly: Q1 = 8 and Q3 = 23. The full set has an even length, so Q2 is the mean of the two central values: (15 + 16) / 2 = 15.5. The IQR is Q3 minus Q1 = 23 - 8 = 15.
The Tukey fences then land at Q1 - 1.5 x IQR = 8 - 22.5 = -14.5 and Q3 + 1.5 x IQR = 23 + 22.5 = 45.5. Every value from 4 to 42 sits inside those bounds, so this dataset has no flagged outliers. If you replaced 42 with 60, the upper fence at 45.5 would flag it.
Quartile methods differ: why your answer may not match
This tool uses the exclusive (Moore and McCabe) method: split the sorted data at the median and take each half's median. That matches most textbooks and AP Statistics, but Excel's QUARTILE.EXC and R's quantile type 6 use a different interpolation scheme, and Excel's default QUARTILE.INC includes the median in both halves. On the same six-value dataset above, all methods happen to agree on Q1 = 8 and Q3 = 23, but with 5 values such as 1, 2, 3, 4, 5 the inclusive method still gives Q1 = 2 and Q3 = 4 while exclusive methods interpolate to Q1 = 1.75 and Q3 = 4.25.
Two consequences follow. First, small datasets amplify the disagreement: a 5-point sample can shift Q1 by 0.25 or more between tools, while a 500-point sample barely moves. Second, when you report quartiles alongside software output, state the method. The IQR inherits the same sensitivity, so a 15 vs 15.5 IQR gap changes the Tukey fences and can flip one borderline value from inlier to outlier.
Also note the tool parses comma, space, and semicolon separators but silently drops non-numeric tokens. Pasting '12, N/A, 18' computes on 12 and 18 only; check the displayed n against your source row count.
