Five Number Summary Calculator

The five-number summary is the minimum, first quartile (Q1), median, third quartile (Q3) and maximum. Enter your data to get all five with the working, a box-and-whisker plot drawn to scale, and any outliers flagged.

IQR
28
Minimum
6
Q1
15
Median (Q2)
40
Q3
43
Maximum
49
Lower fence
−27
Upper fence
85
Q1 15M 40Q3 43
Box plot. Whiskers reach the most extreme values inside the fences; red circles are outliers.
−20020406080
▲ mean 33.1818 · ◆ median 40

Step-by-step working

  1. Sort the data6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49
  2. Find the median (Q2) of all 11 valuesQ2 = 40
  3. n is odd, so leave the median out and split the data into a lower and upper halflower: 6, 7, 15, 36, 39 upper: 41, 42, 43, 47, 49
  4. Q1 is the median of the lower half; Q3 is the median of the upper halfQ1 = 15, Q3 = 43
  5. Interquartile range = Q3 − Q1IQR = 43 − 15 = 28
  6. Fences: 1.5 × IQR below Q1 and above Q3lower = 15 − 1.5 × 28 = −27 upper = 43 + 1.5 × 28 = 85
  7. Any value outside the fences is an outlierNone — every value is inside the fences

Note: Excel’s QUARTILE.INC (and some textbooks) interpolate instead, giving Q1 = 25.5 and Q3 = 42.5. Both are accepted methods; use the one your course teaches.

Formula min · Q1 · median · Q3 · max

Ask the tutor about your result

An AI tutor reads your inputs and results above and explains them in plain English. The numbers come from the calculator; the explanation is AI-written, so check it against your notes.

How to find the five-number summary

  1. Sort the data. The first and last values are the minimum and maximum.
  2. Find the median of the whole list.
  3. Split the list into a lower and an upper half (leave the median out when n is odd).
  4. Q1 is the median of the lower half, Q3 the median of the upper half.

This median-of-halves method matches the TI-83/84 1-Var Stats output and most introductory textbooks. Excel’s QUARTILE.INC interpolates and can differ slightly; the calculator shows both when they disagree.

Drawing a box and whisker plot

Draw a box from Q1 to Q3 with a line at the median. The whiskers run out to the smallest and largest values that are not outliers; values beyond 1.5 × IQR from the box are plotted as separate points. Check them on the outlier calculator.

Frequently asked questions

What does the five-number summary tell you?

Where the middle of the data is (median), how spread out the middle half is (Q1 to Q3, the IQR), and how far the extremes reach. Uneven gaps hint at skew.

Why does my textbook get a different Q1 or Q3?

There are several quartile conventions. This calculator uses median of halves (exclusive); Excel and some books interpolate. Both are legitimate; use the one your course specifies.

Is the box plot whisker the minimum?

Only when there are no low outliers. In a modified box plot the whisker stops at the smallest value inside the lower fence.