5 Number Summary Calculator
The five-number summary describes a dataset with five points: the minimum, first quartile (Q1), median, third quartile (Q3) and maximum. Paste a list of numbers and this calculator sorts them, finds each value and also reports the interquartile range (IQR = Q3 − Q1). These five numbers are exactly what a box-and-whisker plot is built from, giving a quick picture of a distribution's centre and spread.
Formula
Min, Q1, Median (Q2), Q3, Max · IQR = Q3 − Q1
Example Calculation
Inputs
- Numbers (comma-separated): 5,15,20,35,40,45,50,55,60,70,75
For the 11 sorted values 5, 15, 20, 35, 40, 45, 50, 55, 60, 70, 75 the minimum is 5 and the maximum is 75. The median (Q2) is the 6th value, 45. Q1 is the median of the lower five values (20) and Q3 the median of the upper five (60), so the IQR is 60 − 20 = 40.
Frequently asked questions
What is a five-number summary?
It is a set of five values that summarise a dataset: the minimum, first quartile (Q1), median, third quartile (Q3) and maximum.
How are the quartiles calculated here?
The data is sorted, then the median splits it in half. Q1 is the median of the lower half and Q3 the median of the upper half. With an odd count the overall median is excluded from each half.
What is the interquartile range (IQR)?
The IQR is Q3 minus Q1, the spread of the middle 50% of the data. It is a robust measure of dispersion that ignores extreme values.
How does this relate to a box plot?
A box-and-whisker plot draws directly from these five numbers: the box spans Q1 to Q3 with a line at the median, and the whiskers reach the minimum and maximum.
Can quartile methods give different answers?
Yes. There are several conventions for computing quartiles. This calculator uses the exclusive median method, so results may differ slightly from tools that use a different rule.