The Interquartile Range (IQR) Calculator finds the spread of the middle 50% of a data set by calculating the first quartile (Q1), median (Q2), third quartile (Q3), and the IQR (Q3 − Q1).
The IQR is a powerful way to measure variability while ignoring extreme values, making it especially useful in real-life data analysis and school statistics.
What does the calculator do?
- Sorts the data set in ascending order.
- Finds quartiles:
Q1 = lower quartile (25th percentile)
Q2 = median (50th percentile)
Q3 = upper quartile (75th percentile) - Calculates the IQR = Q3 − Q1.
- Displays results clearly for Q1, Q2, Q3, and IQR.
- Copy results with one click for easy use in assignments.
Worked examples
Example 1 — Small set
Data: 6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49
- Q1 = 15
- Q2 = 40
- Q3 = 43
- IQR = 43 − 15 = 28
Example 2 — Even set
Data: 10, 20, 30, 40, 50, 60, 70, 80
- Q1 = 25
- Q2 = 45
- Q3 = 65
- IQR = 65 − 25 = 40
Example 3 — Real-life salaries ($000)
Data: 28, 30, 32, 34, 36, 38, 40, 120
- Q1 = 31
- Q2 = 35
- Q3 = 39
- IQR = 39 − 31 = 8
This shows the middle 50% of salaries (31k–39k), ignoring the outlier (120k).
Why is it important?
- In school: Introduces quartiles, medians, and a robust measure of spread.
- In real life: Used in finance, research, and business to describe data without being misled by extreme outliers.
- In advanced statistics: Forms the basis for boxplots, detecting outliers, and non-parametric analysis.
Frequently Asked Questions
Q1: Why is IQR better than range?
IQR ignores extreme values and focuses on the middle 50%, so it’s less affected by outliers.
Q2: Can I use decimals or negative numbers?
Yes. The calculator works with any real numbers.
Q3: What does a large IQR mean?
It means the data in the middle 50% is widely spread out.
Q4: What does a small IQR mean?
It means the middle 50% of the data is tightly clustered.