The interquartile range measures statistical dispersion by calculating the distance between the first and third quartiles.
Mathematically, it equals the third quartile minus the first quartile, encompassing the middle fifty percent of ordered values.
By focusing strictly on the central half of observations, the interquartile range eliminates the influence of extreme tails.
For example, if Q1 equals forty marks and Q3 equals seventy marks, the interquartile range is thirty marks.
The interquartile range has a breakdown point of twenty-five percent, remaining stable even if quarter of observations are corrupt.
This resilience makes it a robust measure of spread for asymmetric data like household incomes and website visit durations.
The interquartile range forms the core engine of the standard box plot created by statistician John Tukey.
In a box plot, the central rectangular box spans from Q1 to Q3, with a line marking the median inside.
Tukey established a widely adopted heuristic for identifying outliers based on the interquartile range.
The lower fence is defined as Q1 minus 1.5 times the interquartile range.
The upper fence is defined as Q3 plus 1.5 times the interquartile range.
Any observation falling beyond these fences is classified as a potential outlier and plotted as an individual point.
Setting fences at three times the interquartile range identifies extreme outliers that warrant urgent inspection.
Unlike standard deviation, the interquartile range does not inflate when a single extreme observation enters the dataset.
Analysts should use the interquartile range whenever reporting the median, pairing robust location with robust dispersion.