First Quartile (Q1) Calculator

Find the first quartile (Q1) — the 25th percentile — of your data. Paste your numbers to get Q1, the median (Q2), Q3, and the interquartile range.

Quick Facts

Method
Median of the lower half (25th percentile)
Sort the data, split at the median, then take the median of the lower half — Q1.

Your Results

Calculated
First quartile (Q1)
-
25th percentile
Median (Q2)
-
50th percentile
Third quartile (Q3)
-
75th percentile
Interquartile range (IQR)
-
Q3 − Q1

Ready

Enter your numbers and press Calculate.

What the first quartile (Q1) is

The first quartile, written Q1, is the value that separates the lowest 25% of a dataset from the top 75% once the numbers are sorted from smallest to largest. It is also called the lower quartile or the 25th percentile. Together with the median (Q2, the 50th percentile) and the third quartile (Q3, the 75th percentile), it divides the data into four groups that each hold about one quarter of the values.

Q1 is a positional statistic: it depends only on the order of the values, not on how large the extremes are. That makes it resistant to outliers, which is why quartiles are the backbone of box-and-whisker plots and of the standard outlier rule (a point below Q1 − 1.5·IQR or above Q3 + 1.5·IQR).

How this calculator computes Q1

It uses the median-of-halves method (also known as Tukey's hinges, the "exclusive" method used in many introductory statistics courses):

  1. Sort all the numbers in ascending order.
  2. Find the median (Q2). If the count is odd, the single middle value is the median and is not placed in either half.
  3. Take the lower half — every value below the median position — and find its median. That is Q1. The median of the upper half is Q3.

Worked example with 9 sorted values: 3, 5, 7, 8, 12, 13, 14, 18, 21. The median is the 5th value, 12. The lower half is 3, 5, 7, 8, and its median is (5 + 7) / 2 = 6, so Q1 = 6. The upper half is 13, 14, 18, 21, so Q3 = (14 + 18) / 2 = 16, and the IQR is 16 − 6 = 10.

A note on methods

Quartiles have no single universal definition. This tool's median-of-halves result can differ slightly from a spreadsheet's built-in function. Excel's QUARTILE / QUARTILE.INC uses linear interpolation at position (n−1)·0.25 + 1, and QUARTILE.EXC uses position (n+1)·0.25; R offers nine "types." For most datasets the differences are small, and any of these methods is defensible as long as you report which one you used.

Common reference points

  • Q1 = 25th percentile. A quarter of the data is at or below it.
  • IQR = Q3 − Q1 spans the middle 50% of the data and is the standard robust measure of spread.
  • Five-number summary: minimum, Q1, median, Q3, maximum — the values a box plot draws.
  • Outlier fences: lower fence = Q1 − 1.5·IQR, upper fence = Q3 + 1.5·IQR.

Frequently Asked Questions

What is the first quartile (Q1)?
Q1 is the value below which 25% of your data falls once the numbers are sorted. It is the 25th percentile and the median of the lower half of the dataset. It marks the boundary between the bottom quarter and the top three quarters.
How is Q1 different from the minimum or the median?
The minimum is the single smallest value (0th percentile). The median (Q2) is the middle value (50th percentile). Q1 sits between them at the 25th percentile — a quarter of the values are below it and three quarters are above it.
Why does my spreadsheet give a slightly different Q1?
Different tools use different quartile definitions. This calculator uses the median-of-halves method (excluding the overall median when the count is odd). Excel's default QUARTILE.INC interpolates at position (n−1)·0.25 + 1, which can land between two data points and produce a slightly different value. Both answers are valid — just be consistent about which method you report.
Do I need to sort my data first?
No. This calculator sorts the numbers for you and shows the sorted list under the result, so you can enter them in any order, separated by commas, spaces, or new lines.

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