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📘 About the Interquartile Range
Quartiles split sorted data into four equal parts. Q1 is the median of the lower half, Q2 the median, Q3 the median of the upper half. The interquartile range IQR = Q3 − Q1 is the spread of the middle 50% of the data — a measure of spread that, unlike the range, ignores extreme values.
Paste your data. The calculator sorts it, shows the lower and upper halves, gives Q1, Q2, Q3 and the IQR, the five-number summary for a box plot and the 1.5 × IQR outlier fences, and also Excel’s QUARTILE.INC values, which use a slightly different method.
🧮 Formula
✏️ Worked examples
11 values
You get| Interquartile range (IQR) | 10 |
| Q1 (lower quartile) | 5 |
| Q2 (median) | 10 |
| Q3 (upper quartile) | 15 |
| Five-number summary | min 1 · Q1 5 · median 10 · Q3 15 · max 29 |
| Outlier fences (1.5 × IQR) | below −10 or above 30 |
| Semi-interquartile range | 5 |
| Excel QUARTILE.INC method | Q1 = 6, Q3 = 14, IQR = 8 |
IQR = 10.
Even number of values
You get| Interquartile range (IQR) | 34.5 |
| Q1 (lower quartile) | 11.5 |
| Q2 (median) | 19.5 |
| Q3 (upper quartile) | 46 |
| Five-number summary | min 4 · Q1 11.5 · median 19.5 · Q3 46 · max 61 |
| Outlier fences (1.5 × IQR) | below −40.25 or above 97.75 |
| Semi-interquartile range | 17.25 |
| Excel QUARTILE.INC method | Q1 = 13.25, Q3 = 44, IQR = 30.75 |
IQR = 34.5.
🧭 How to use this calculator
What you enter
- DataSeparate numbers with commas, spaces or new lines.
What you get
- Interquartile range (IQR)
- Q1 (lower quartile)
- Q2 (median)
- Q3 (upper quartile)
- Five-number summary
- Outlier fences (1.5 × IQR)
- Semi-interquartile range
- Excel QUARTILE.INC method
❓ Frequently asked questions
How do you find Q1 and Q3?
Sort the data, split it at the median, and find the median of each half. With an odd count, leave the median out of both halves.
Why do calculators give different quartiles?
There are several conventions. Schools and TI calculators use medians of halves; Excel’s QUARTILE.INC interpolates. Both are shown.
What does the IQR tell you?
How spread out the middle half of the data is. It is resistant to outliers, so it suits skewed data.
