Quartile Calculator
Find Q1, Q2, Q3, and the interquartile range (IQR) for any list of numbers.
How it works
- 1Enter your numbers separated by commas or spaces — the list is parsed automatically.
- 2The calculator sorts the data and uses linear interpolation to find the 25th, 50th, and 75th percentiles (Q1, Q2, Q3).
- 3IQR is computed as Q3 − Q1, capturing the spread of the middle 50% of your data.
Use cases
- Identify outliers: values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR are flagged in box-plot analysis.
- Summarise grade distributions to understand how students cluster around the median.
- Analyse financial or sensor data to measure variability without being skewed by extremes.
Frequently asked questions
What do the quartiles represent?
Quartiles divide a sorted dataset into four equal parts. Q1 is the 25% boundary, Q2 (the median) splits the data in half, and Q3 is the 75% boundary. Each interval holds about 25% of the data.
Why does this calculator use linear interpolation?
There are several accepted methods for quartiles. This tool uses the continuous linear-interpolation method (the default in NumPy and many packages), giving smooth, consistent results for any dataset size.
What is the IQR used for?
The interquartile range measures the spread of the central 50% of the data. Because it ignores the lowest and highest quarters, it resists outliers — a more robust measure of variability than the full range.
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