Quartile Calculator

Worked example

Dataset: 7, 15, 36, 39, 40, 41 (n = 6, already sorted).

• Median (50th percentile): position = 0.50 × (6−1) = 2.5, halfway between index 2 (36) and index 3 (39) → (36 + 39) / 2 = 37.5
• Q1 (25th percentile): position = 0.25 × 5 = 1.25, 25% of the way from index 1 (15) to index 2 (36) → 15 + 0.25×(36−15) = 20.25
• Q3 (75th percentile): position = 0.75 × 5 = 3.75, 75% of the way from index 3 (39) to index 4 (40) → 39 + 0.75×(40−39) = 39.75
• IQR = Q3 − Q1 = 39.75 − 20.25 = 19.5

Which quartile method this uses

There isn't one universal definition of a quartile — statistics software disagrees on the method. This calculator uses linear interpolation between closest ranks (the same approach as Excel's PERCENTILE.INC and NumPy's default percentile), computing a fractional position in the sorted list and interpolating between the two nearest values. This differs from the older Tukey "hinges" method (splitting the dataset at the median and taking the median of each half), which on this same dataset would give Q1 = 15 and Q3 = 40 instead. If you're cross-checking against a textbook or another tool, confirm which method it uses before assuming a mismatch is an error.

Minimum data requirement

At least 3 numeric values are required — with fewer, quartile positions can't meaningfully interpolate. Non-numeric entries in the input (stray text, empty tokens) are silently filtered out before the count is taken.