IQR Calculator (Interquartile Range)
Enter your data set below to find Q1, median (Q2), Q3, IQR, and potential outliers using the 1.5×IQR rule.
What is IQR and why does it matter?
The interquartile range (IQR) measures the spread of the middle 50% of your data. It is calculated as:
IQR = Q3 − Q1
Where Q1 is the first quartile (25th percentile) and Q3 is the third quartile (75th percentile). Unlike the full range (max − min), IQR is less sensitive to extreme values, so it gives a more stable picture of variability.
How to calculate IQR on a calculator
Method 1: Use the calculator tool above
- Paste or type your values into the input box.
- Choose a quartile method (Tukey or Linear).
- Click Calculate IQR.
- Read Q1, median, Q3, IQR, fences, and outliers instantly.
Method 2: Do it manually with any basic calculator
- Sort numbers from smallest to largest.
- Find the median (Q2).
- Find Q1 from the lower half and Q3 from the upper half.
- Subtract: IQR = Q3 - Q1.
This manual approach is useful for homework checks and exam situations where you need to show steps.
Finding IQR on popular graphing calculators
TI-83 / TI-84 steps
- Press STAT → Edit, then enter data into L1.
- Press STAT → arrow to CALC → select 1-Var Stats.
- Use L1 as input and run calculation.
- Scroll through results to find Q1 and Q3.
- Compute IQR by subtracting Q1 from Q3.
Casio calculators (ClassWiz / graphing)
- Open the statistics mode and choose one-variable statistics.
- Input your dataset.
- Run variable summary calculations.
- Locate quartiles (names vary by model), then compute Q3 − Q1.
Menu names differ by model, but the workflow stays the same: enter data, run 1-variable stats, read quartiles, subtract.
How to interpret your IQR result
A larger IQR means the middle half of your observations are more spread out. A smaller IQR means those values are tighter and more consistent.
- Low IQR: central values are clustered.
- High IQR: central values vary more.
- IQR with outliers: use fences to identify unusual points.
Outlier fences
The common rule is:
- Lower fence = Q1 − 1.5 × IQR
- Upper fence = Q3 + 1.5 × IQR
Any value below the lower fence or above the upper fence is often flagged as a potential outlier.
Worked example
Suppose your data are: 4, 7, 8, 9, 10, 12, 13, 18, 25.
- Q1 = 7.5 (depending on method)
- Q3 = 15.5 (depending on method)
- IQR = 8.0
- Lower fence = -4.5
- Upper fence = 27.5
In this set, 25 is high but still inside the upper fence, so it is not an outlier under the 1.5×IQR rule.
Common mistakes when calculating IQR
- Not sorting the data first.
- Mixing quartile definitions from different software.
- Using range instead of IQR when outliers are present.
- Forgetting to show which quartile method you used.
If your answer differs from a textbook or spreadsheet, check the quartile definition first. Different methods can produce slightly different Q1 and Q3 values.
Quick FAQ
Is IQR the same as standard deviation?
No. Standard deviation uses all values and is sensitive to outliers, while IQR focuses on the middle 50%.
Can IQR be zero?
Yes. If Q1 and Q3 are equal (common in repeated values), IQR is zero.
Which quartile method should I use?
Use the method required by your class, instructor, or software. For consistency across reports, always document the method used.