Summary: This five number summary calculator computes quartiles, IQR and box plot with live steps, formulas and a chart. It accepts labeled numeric inputs, works offline through file:// and includes source-backed explanations for students, analysts and researchers.
Five number summary calculator for min, Q1, median, Q3, max, IQR, fences, outliers and live box plot. The calculator works offline, updates instantly and includes a worked example, plain-text formula, MathML, references and structured data.
Default values are loaded. Click any field and edit it; results and chart update automatically.
| Input or setting | Result or interpretation | Use this when |
|---|---|---|
| Method | R/NumPy type 7 quantiles | quartile summary |
| IQR | Q3 - Q1 | quartile summary |
| outliers | outside 1.5 * IQR fences | quartile summary |
five number summary = min, Q1, median, Q3, max; IQR = Q3 - Q1; fences = Q1 - 1.5*IQR and Q3 + 1.5*IQRThe five number summary describes the minimum, lower quartile, median, upper quartile and maximum.
2,5,7,8,10,13,14,15,17,20
min=2, Q1=7.25, median=11.5, Q3=14.75, max=20, IQR=7.5, no outliers
This page uses the shared statistics core for distribution functions, quantiles and exact integer counting where needed. The formula is shown in plain text so screen readers and search engines can parse it reliably.
Use Load example in the calculator to reproduce this reference result.
{
"tool": "Five Number Summary Calculator",
"input": "2,5,7,8,10,13,14,15,17,20",
"output": "min=2, Q1=7.25, median=11.5, Q3=14.75, max=20, IQR=7.5, no outliers",
"formula": "five number summary = min, Q1, median, Q3, max; IQR = Q3 - Q1; fences = Q1 - 1.5*IQR and Q3 + 1.5*IQR"
}| Calculator | Example input | Expected output |
|---|---|---|
| Five Number Summary Calculator | 2,5,7,8,10,13,14,15,17,20 | min=2, Q1=7.25, median=11.5, Q3=14.75, max=20, IQR=7.5, no outliers |
What does p = 0.03 mean? If the null hypothesis and model assumptions were true, a result at least this extreme would occur about 3% of the time. The American Statistical Association cautions that a p-value alone does not measure effect size, practical importance or the probability that Hâ‚€ is true.3
For most classroom and professional reports, pair the calculator result with the question you are answering. A mean or median summarizes location, but spread explains consistency. A confidence interval estimates plausible values, while a hypothesis test evaluates compatibility with a null model. Regression and correlation describe association, so they should be reported with a chart and residual or outlier review. When a result is statistically significant, still ask whether the effect is large enough to matter in the real setting.
| Statistic | Small | Medium | Large | Use |
|---|---|---|---|---|
| Cohen's d | 0.2 | 0.5 | 0.8 | t-test effect size |
| Cramér's V | 0.1 | 0.3 | 0.5 | chi-square association |
| |r| | 0.10 | 0.30 | 0.50 | correlation strength |
| R² | 0.01 | 0.09 | 0.25 | variance explained |
Sort your data from smallest to largest, then identify five values: the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. Q1 is the median of the lower half, Q3 the median of the upper half. Example with 7 values {3, 5, 7, 9, 11, 13, 15}: min = 3, Q1 = 5, median = 9, Q3 = 13, max = 15. These five numbers capture the centre, spread, and shape of your data, and they're exactly what you need to draw a box plot.
After sorting, split the data at the median. Q1 is the median of the lower half; Q3 is the median of the upper half. The catch: with an odd number of values, some methods exclude the overall median from both halves (Tukey's method) while others include it (the inclusive method). For {1, 3, 5, 7, 9}, exclusive gives Q1 = 2, Q3 = 8; inclusive gives Q1 = 3, Q3 = 7. Different calculators use different conventions, which is why answers can vary slightly — always check which method is used.
The five numbers map directly onto the diagram. Draw a horizontal axis covering the data range. The minimum and maximum become the ends of the two whiskers. Q1 and Q3 form the left and right edges of the box. The median is drawn as a vertical line inside the box. The box itself shows where the middle 50% of values sit, and the whiskers stretch out to the extremes. If you want to flag outliers, plot any points beyond Q1 − 1.5 × IQR or Q3 + 1.5 × IQR as separate dots.
Use the 1.5 × IQR rule. First, compute IQR = Q3 − Q1. Then build two fences: lower = Q1 − 1.5 × IQR, upper = Q3 + 1.5 × IQR. Any data point outside these fences is considered an outlier. Suppose Q1 = 20, Q3 = 40, so IQR = 20. The fences are 20 − 30 = −10 and 40 + 30 = 70. A value of 85 sits above the upper fence, so it's flagged. Some textbooks use 3 × IQR for "extreme" outliers — useful for very skewed data.
The five number summary is a complete snapshot of your data: minimum, Q1, median, Q3, and maximum — five values total. The IQR is just one number derived from that summary: IQR = Q3 − Q1, capturing the spread of the middle 50% of your data. Think of the summary as the full picture and the IQR as one specific measurement taken from it. The IQR is robust against outliers because it ignores the tails entirely, which is why it pairs nicely with the median for skewed distributions.
Just subtract: IQR = Q3 − Q1. Suppose Q1 = 25 and Q3 = 75, then IQR = 50, meaning the middle 50% of your data spans 50 units. The IQR measures variability while ignoring extreme values, which makes it ideal for skewed distributions where standard deviation can be misleading. It's also the foundation for spotting outliers using the 1.5 × IQR fences. A small IQR points to data clustered around the median; a large IQR signals more spread within the bulk of the dataset.
That depends on the convention you're following. The exclusive method (Tukey's hinges, often used in textbooks) drops the overall median when splitting an odd-sized dataset, so it isn't part of either half. The inclusive method keeps the median in both the lower and upper halves. For {2, 4, 6, 8, 10}, exclusive gives Q1 = 3, Q3 = 9; inclusive gives Q1 = 4, Q3 = 8. Excel's QUARTILE.INC uses inclusive; QUARTILE.EXC uses exclusive. Neither is "wrong" — calculators just need to declare which method they apply.
With an odd number of values, the median is the exact middle value once the data is sorted — no averaging needed. Take {2, 5, 7, 9, 11, 13, 15}: that's 7 values, so the median is the 4th value, which is 9. Then split the data into the lower half {2, 5, 7} and upper half {11, 13, 15} (excluding the median itself in Tukey's method). Q1 = 5, Q3 = 13. Min and max are simply 2 and 15. Final summary: 2, 5, 9, 13, 15.