Quartile methods and why calculators disagree
Different methods give different Q1 and Q3 values. See why PERCENTILE.INC, the exclusive method, and the median split disagree.
What a quartile actually is
A quartile is a cut point that divides sorted data into four equal parts. The first quartile (Q1) marks the value below which about a quarter of the data falls, the second is the median, and the third (Q3) sits at roughly three quarters. The trouble is that real data sets rarely divide into four exactly equal groups, so a quartile often lands between two observed values. How a method fills that gap is where different calculators start to disagree.
The interpolation method this tool uses
This calculator uses linear interpolation between the two closest ranks, the same convention as Excel PERCENTILE.INC and NumPy's default percentile. It places a quartile at position (n minus 1) times the percentile on a zero based index, then blends the two neighbouring values by the fractional part. For the set 10, 20, 30, 40 the first quartile lands at position 0.75, three quarters of the way from 10 to 20, which gives 17.5. This inclusive approach always includes the endpoints and gives a smooth, reproducible answer.
The median-split methods
An older family of methods splits the data at the median and takes the median of each half as Q1 and Q3. When the count is odd, some versions include the overall median in both halves (Tukey's hinges) and some exclude it (the exclusive method). These rules can hand back different quartiles than interpolation for the same numbers, which is exactly why two honest calculators sometimes disagree. Neither is wrong; they answer the question with different conventions.
Staying consistent
The practical rule is to pick one method and use it everywhere in a piece of analysis, then state which one you used. Because Excel, Google Sheets PERCENTILE, and NumPy all default to the interpolation method, matching it keeps your quartiles, IQR, and Tukey fences aligned with the most widely used tools. If a report cites quartiles from statistics software that uses a median split, expect small differences and note the method rather than assuming an error.