Quartile & IQR Calculator

Find the quartiles, interquartile range, five-number summary and outliers of a data set.

Data	12, 15, 18, 22, 22, 25, 30, 31, 35, 41

Data

Separate numbers with commas, spaces or new lines.

Q1, Q2 (median), Q3

19, 23.5, 30.75

The middle half of the data runs from 19 to 30.75, an interquartile range of 11.75. No outliers by the 1.5 × IQR rule.

Interquartile range (IQR): 11.75
Five-number summary: 12, 19, 23.5, 30.75, 41
Outlier fences: below 1.375 or above 48.375

Box plot of your data

Q1 19Q3 30.75Box: middle half of the values (Q1 to Q3), line at the median

About the Quartile & IQR Calculator

Quartiles split sorted data into four equal parts. Q1 is the 25th percentile, Q2 the median and Q3 the 75th percentile. The interquartile range, Q3 − Q1, is the spread of the middle half and isn't affected by extreme values. Points more than 1.5 × IQR beyond the quartiles are flagged as possible outliers, the same rule box plots use.

The formula

IQR = Q3 − Q1; outliers < Q1 − 1.5·IQR or > Q3 + 1.5·IQR

Method: linear interpolation (Excel QUARTILE.INC, R type 7)

Worked example

Example: Q1, Q2 (median), Q3 = 7, 12, 14

Input: Data: 3, 7, 8, 5, 12, 14, 21, 13, 18.
Formula: IQR = Q3 − Q1; outliers < Q1 − 1.5·IQR or > Q3 + 1.5·IQR
Result: Q1, Q2 (median), Q3 = 7, 12, 14
Interquartile range (IQR): 7
Five-number summary: 3, 7, 12, 14, 21
Outlier fences: below -3.5 or above 24.5

Questions people ask

Why are there different quartile answers online?

Several definitions exist; for large data sets they agree closely.

What is a box plot?

A chart of the five-number summary: min, Q1, median, Q3, max.