↔️ Interquartile Range Calculator
Calculate the interquartile range and middle 50% spread of a dataset.
📊 Statistics📐 Formula included🧠 Practice questions✓ Free
Please enter valid values.
Formula and Explanation
Calculate the interquartile range and middle 50% spread of a dataset.
| Concept | Formula or rule |
|---|---|
| Interquartile Range Calculator | IQR = Q₃ − Q₁ |
How to Use This Calculator
- Enter the sample, counts, probabilities, or summary statistics requested above.
- Keep paired lists in the same order and separate values with commas.
- Select the correct test direction or sample/population option when available.
- Press Calculate and interpret the result together with the supporting statistics.
Worked Example
Example: If Q1 = 10 and Q3 = 22, then the middle half of the data spans 12 units.
✓ IQR = 22 − 10 = 12
Where This Is Used
School & coursework
Check homework, understand formulas, and verify step-by-step statistics exercises.
Research
Explore estimates, uncertainty, distributions, and relationships before using full statistical software.
Business & data analysis
Summarize variation, compare groups, and communicate data-driven findings clearly.
Common Mistakes to Avoid
⚠️
Using maximum minus minimum
That is the range, not the interquartile range.
That is the range, not the interquartile range.
⚠️
Changing quartile methods mid-analysis
Use one quartile convention consistently.
Use one quartile convention consistently.
⚠️
Ignoring skewness
IQR is robust, but its position relative to the median also contains information.
IQR is robust, but its position relative to the median also contains information.
Practice Questions
1. Q1=4 and Q3=10. Find IQR.
Answer: 6
2. Which is more resistant to outliers: range or IQR?
Answer: IQR.
3. What portion of data is summarized by IQR?
Answer: The middle 50%.
Frequently Asked Questions
Why use IQR?▾
It measures spread without being strongly affected by extreme values.
Can IQR be zero?▾
Yes, when Q1 and Q3 are equal.
How is IQR used for outliers?▾
Common fences are Q1 − 1.5×IQR and Q3 + 1.5×IQR.