Paste numbers, pick quartile rule, get IQR fast. See fences, outliers, and clean summaries now. Export tables to share, print, and study later securely.
| Dataset | Q1 | Q3 | IQR | Lower fence (k=1.5) | Upper fence (k=1.5) |
|---|---|---|---|---|---|
| 2, 4, 7, 9, 10, 12, 13, 15, 18, 21, 22 | 7.000 | 18.000 | 11.000 | -9.500 | 34.500 |
The interquartile range measures the spread of the middle 50% of values: IQR = Q3 − Q1.
For a dataset of n values, Q1 marks the 25th percentile and Q3 marks the 75th percentile. The interquartile range is IQR = Q3 − Q1, so it summarizes the spread of the central 50% without being pulled by extreme points. In many classroom datasets, Tukey’s median-of-halves method is preferred because it is transparent and easy to verify by hand.
The range uses only the minimum and maximum, so one unusual observation can inflate it dramatically. IQR focuses on the middle half, which makes it stable when a few values are far away. For example, if most values sit between 40 and 60 but one value is 200, the range grows by 160, while IQR often changes only slightly.
This calculator also reports Tukey fences: Lower = Q1 − k·IQR and Upper = Q3 + k·IQR. The common choice k = 1.5 flags “regular” outliers, while k = 3.0 is used for “far” outliers in some reporting standards. If IQR is 8 and Q1 is 42, then with k = 1.5 the lower fence is 42 − 12 = 30.
Different tools compute quartiles using different interpolation rules, especially for small samples. Inclusive interpolation matches many spreadsheet percentile functions, while exclusive interpolation can return undefined quartiles when the sample is tiny. To keep results reproducible, this page lets you choose a method and then exports the same computed values to CSV and PDF.
The Plotly box plot visualizes the five-number summary: minimum, Q1, median, Q3, and maximum, plus outliers beyond the fences. The box height equals IQR, so taller boxes indicate more variability. Points plotted outside the whiskers are potential outliers; confirm them with context rather than removing them automatically.
IQR is widely used for quick quality checks in measurement, finance, and performance logs. Analysts often compare IQR across groups to spot volatility shifts, for example weekly response times or monthly sales dispersion. Because IQR is unit-consistent, it works on seconds, dollars, or temperatures alike, and it pairs naturally with median-based summaries. It is simple, fast, and auditable.
IQR measures the spread of the middle 50% of values. It is less sensitive to extreme points than the range, so it gives a stable sense of typical variability.
Use Tukey when you need a clear, hand-checkable approach. Use Inclusive when matching common spreadsheet percentile outputs. Use Exclusive only if your workflow explicitly requires it.
Exclusive interpolation can be undefined for very small samples because the percentile position falls outside the data index range. Add more observations or switch to Tukey or Inclusive.
No. Outliers are signals for review. They may be data entry mistakes, rare events, or meaningful extremes. Validate with context and document any cleaning decisions.
k scales the fences around Q1 and Q3. Larger k flags fewer outliers; smaller k flags more. Common practice uses k=1.5 for regular outliers and k=3 for far outliers.
CSV and PDF are generated from the latest computed summary shown on the page. Recalculate after changing inputs to ensure the exported file matches your selected method and rounding.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.