Interquartile Range Calculator

Calculate Q1, median, Q3 and the interquartile range of a data set

Quartiles use the median-of-halves method.

Your result will appear here.

About the Interquartile Range Calculator

The interquartile range measures the spread of the middle 50% of a data set. It is the difference between the third quartile and first quartile and is less sensitive to extreme values than the full range.

IQR is commonly used with box plots and outlier rules because it focuses on the central half of the ordered data.

How to Use the Interquartile Range Calculator

  1. Enter the numerical data set.
  2. Calculate the first quartile Q1 and third quartile Q3.
  3. Subtract Q1 from Q3 to obtain the IQR.
  4. Use the same quartile convention when comparing results from different software.

How the Calculation Works

IQR = Q3 − Q1. The data are sorted, then quartiles are located using the calculator’s selected percentile or median-of-halves convention.

Potential outlier fences are often estimated as Q1−1.5×IQR and Q3+1.5×IQR, although that rule is a descriptive convention rather than proof that a value is erroneous.

Worked example

Interquartile Range Calculator Worked Example

Data 1, 2, 3, 4, 5, 6, 7, 8

Using the median-of-halves approach, Q1=(2+3)÷2=2.5 and Q3=(6+7)÷2=6.5. IQR=6.5−2.5=4.

Result guide

Understanding Your Interquartile Range Calculator Result

A larger IQR means the central half of the data is more spread out. Extreme minimum or maximum values do not directly change the IQR unless they affect quartile positions.

Before you rely on the answer

Assumptions and Limitations

  • The quartile convention is consistent.
  • Values belong to one comparable data set.
  • Outlier fences are descriptive thresholds, not automatic deletion rules.

Practical tip

Using This Result in Practice

Use IQR alongside a plot or ordered list. A flagged outlier may be a valid unusual observation rather than a data error.

Related calculations

Useful Calculations to Continue With

If you need a percentile other than the first or third quartile, use the Percentile Calculator.

If you want a spread measure that uses every value and is centered on the mean, use the Standard Deviation Calculator.

Authoritative references

Useful Official Sources

For standards, definitions or real-world guidance related to this calculation, these primary sources may be useful:

Common questions

Interquartile Range Calculator FAQ

What does IQR measure?

It measures the width of the middle 50% of ordered observations: Q3 minus Q1.

Why is IQR resistant to outliers?

It depends on the central quartiles rather than directly using the minimum and maximum.

What is the 1.5×IQR rule?

It creates lower and upper fences often used to flag potentially unusual observations in box-plot analysis.