Range & Interquartile Range Calculator
Enter any set of numbers — get the range, IQR, quartiles, and a box plot with full step-by-step working.
Range & IQR calculator
Step-by-step solution
Enter a data set and press Calculate
Range & Interquartile Range Calculator Explained
Core concepts, classroom applications, and plain-English explanations for all audiences.
Where you already use range
A week's weather forecast shows a high of 18°C and a low of 9°C — the range is 9°C. A job advert lists £28,000–£35,000 — the salary range is £7,000. A football team's season scores ran from 0 to 5 goals — the range is 5. Range is the gap between the biggest and smallest value in any dataset.
Worked example
"Daily step counts for a week: 6,400 — 9,200 — 7,800 — 11,500 — 8,100 — 5,600 — 10,300. What is the range?"
Step 1: Find the maximum — 11,500
Step 2: Find the minimum — 5,600
Step 3: Range = 11,500 − 5,600
Result: Range = 5,900 steps
You don't need to sort the data to find the range — just spot the highest and lowest values.
Common mistake to avoid
- ✗ Confusing range with mean: range tells you how spread out data is, not the typical value. A class scoring 60–80% has a small range; one scoring 10–95% has a large range — even if both have the same mean.
Understanding spread in statistics
Range
The simplest measure of spread: maximum minus minimum. Easy to calculate but heavily affected by outliers.
Interquartile Range (IQR)
The range of the middle 50% of data (Q3 − Q1). Resistant to outliers and used to define formal outlier thresholds.
Quartiles (Q1, Q2, Q3)
Q1 divides bottom 25%, Q2 is the median (50%), and Q3 divides top 25%. Forms the core box of box-and-whisker plots.