Quartile Calculator

First quartile (Q1), median (Q2) and third quartile (Q3) — with worked steps

Enter your data to find the three quartiles — Q1, Q2 (the median) and Q3 — along with the interquartile range and a step-by-step solution.

Enter Your Data Points

Textbooks differ — pick the method yours uses.

Results

Q1 (25th)21
Q2 / Median29.5
Q3 (75th)37.5

Five Number Summary

Minimum9
Q1 (25th)21
Median29.5
Q3 (75th)37.5
Maximum48
Interquartile range (IQR)16.5
Count (n)20
Outliers (1.5 × IQR rule)None

Additional Statistics

Mean (average)29.1
Mode21
Range39
Sum582
Std deviation (sample)10.8235
Std deviation (population)10.5494
Variance (sample)117.1474
Mean absolute deviation8.9
Coefficient of variation0.3719
Standard error of the mean2.4202
10th percentile16.5
90th percentile42.2
Lower inner fence (Q1 − 1.5·IQR)-3.75
Upper inner fence (Q3 + 1.5·IQR)62.25

Box & Whisker Plot

Histogram

Step-by-step solution

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What are quartiles?

Quartiles split a sorted data set into four equal parts. The first quartile (Q1) is the 25th percentile — a quarter of the values fall below it. The second quartile (Q2) is the 50th percentile, which is simply the median. The third quartile (Q3) is the 75th percentile, with three quarters of the values below it. Together with the minimum and maximum, the quartiles form the five-number summary.

How to find Q1 and Q3

Sort the data and locate the median (Q2). The median of the lower half of the data is Q1, and the median of the upper half is Q3. The only subtlety is what to do with the middle value when the count is odd: the Tukey method excludes it from both halves, while the Moore & McCabe method includes it. Excel’s QUARTILE.INC instead interpolates between positions. You can switch methods above to match whichever your textbook or software uses.

Reading the quartiles

The gap between Q1 and Q3 — the interquartile range — shows where the central half of the data lies. If the median sits closer to Q1 than to Q3, the data is right-skewed; closer to Q3 means left-skewed. The box plot above draws the quartiles directly: the box runs from Q1 to Q3 with a line at the median.

Frequently asked questions

What is Q2?

The second quartile (Q2) is the median of the data — the 50th percentile, the value that splits the data set in half.

Why do different tools give different quartiles?

There are several accepted methods for computing quartiles (Tukey, Moore & McCabe, and interpolation) that differ in how they treat the median for odd-sized data sets. This calculator supports all three so you can match your source.

What is the interquartile range?

The interquartile range is Q3 − Q1, the spread of the middle 50% of the data. It is shown alongside the quartiles above.

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