How to use this IQR calculator
Enter your data above and press Calculate. Along with the interquartile range you will see Q1, Q3 and the fences used to spot outliers.
What is the interquartile range?
The IQR is the width of the middle half of your data: Q3 minus Q1. Where the full range stretches from the single smallest to the single largest value, and can be wrecked by one freak result, the IQR ignores the extreme quarters entirely and measures only the spread of the typical middle. It is the median's natural partner: median for location, IQR for spread.
The quiz class again: 58, 72, 65, 80, 91, 67, 72, 74, 69, 72. With Q1 = 67.5 and Q3 = 73.5, the IQR = 6 marks. Compare that with the standard deviation (about 8.8): the SD is inflated by the 58 and the 91 at the edges, while the IQR calmly reports that the middle half of the class fits inside a 6-mark band. Both numbers are honest; they answer different questions.
The 1.5 × IQR outlier rule
Build two fences: Q1 − 1.5×IQR and Q3 + 1.5×IQR. Any value outside them is flagged as an outlier: worth a look, not an automatic deletion. For the quiz class the fences are 58.5 and 82.5, so both the 58 and the 91 get flagged. The rule comes from John Tukey and draws the whiskers of every box plot you have ever seen.
Frequently asked questions
What does the interquartile range tell you?
How spread out the middle 50% of your data is. A small IQR means the typical values are tightly packed; a large IQR means they vary widely, ignoring extremes.
How is IQR different from range?
The range uses only the minimum and maximum, so one extreme value can dominate it. The IQR uses quartiles and is resistant to outliers.
What is the 1.5 IQR rule?
Values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR are flagged as potential outliers. It is a screening rule from exploratory data analysis, not proof that a value is wrong.