How this instrument works
The first quartile, Q1, is the value below which roughly a quarter of your sorted data falls. It's the boundary of the lowest-scoring, lowest-valued, or lowest-measured fourth of whatever you're looking at — exam scores, response times, delivery delays, wages in a department. Where the median splits data in half, Q1 splits off just the bottom slice, which is exactly the number you want when the question is specifically about the low end rather than the whole spread.
This instrument computes Q1 by linear interpolation between the two closest ranked values, the method documented by NIST and used by spreadsheet software's PERCENTILE.INC function: sort the data, find the rank position 1 + 0.25 x (n - 1), and interpolate between the values on either side of that position when it falls between two ranks rather than exactly on one. Several other quartile conventions exist and give slightly different answers on small data sets — this page states its method so you can compare like for like.
Q1 shows up whenever someone needs a bottom-quartile threshold rather than a full breakdown: a scholarship fund identifying applicants in the lowest income quarter, a factory flagging the fastest 25% of failure times for a reliability study, or a teacher marking the boundary of the lowest-scoring group for extra support. It's also half of the interquartile range, used with Q3 to measure the spread of the middle half of a data set.
- Paste or type your numbers into the Data set field — commas, spaces or new lines all work.
- Read the Q1 (25th percentile) readout — the value below which the bottom quarter of your entries falls.
- Enter at least two values; the instrument needs a genuine spread to interpolate a rank position from.
- Need Q3 as well, or all three quartiles together? This site's third-quartile and quartile calculators use the same method and return those instead.
Worked example — the eight quiz scores
Take {2, 4, 4, 4, 5, 5, 7, 9}, already sorted, n = 8. The rank position is r = 1 + 0.25 x (8 - 1) = 1 + 1.75 = 2.75, which falls between the 2nd value (4) and the 3rd value (4) in the sorted list.
Both of those neighbouring values happen to be 4, so the interpolation contributes nothing extra: Q1 = 4 + 0.75 x (4 - 4) = 4.0 exactly. A quarter of these eight quiz scores sit at or below 4 — three scores (2, 4, 4) fall in that bottom slice.
Questions
What exactly does the first quartile tell me?
It tells you the value below which about 25% of your sorted data falls. If Q1 of a set of exam scores is 62, roughly a quarter of students scored 62 or below — it's a single threshold marking the bottom fourth, not a range or an average.
Is Q1 the same as the 25th percentile?
Yes, they're exactly the same number — 'first quartile' and '25th percentile' are two names for the identical cut point. Quartile terminology is common in basic statistics and box plots specifically; percentile terminology is more general and lets you ask for any cut point, not just the quarter marks.
Why does my Q1 differ from a textbook's answer for the same data?
Quartiles have at least nine published conventions, and they can disagree on small data sets. This instrument interpolates linearly between closest ranks — the method behind Excel and Google Sheets' PERCENTILE.INC function and the one NIST documents — so if a textbook uses a different method, expect a small difference, not an error.
I need Q1 and Q3 together — should I run this twice?
You can, but it's simpler to use the quartile calculator on this site, which returns Q1, the median (Q2) and Q3 together from a single data entry, using the identical interpolation method as this page — the numbers will always match.
How is Q1 different from the minimum?
The minimum is the single smallest value in your data set; Q1 is a cut point below which about a quarter of the values fall, and it's almost always larger than the minimum unless a quarter or more of your data ties for the lowest value. Confusing the two understates how much of your data actually sits in the bottom slice.