Five-Number Summary Calculator
Enter the five-number summary of a dataset to compute spread metrics and the boxplot outlier fences. The five-number summary provides a complete picture of a distribution's location, spread, and shape.
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Formula
IQR = Q3 − Q1 | Range = Max − Min | Fences = Q1 ± 1.5×IQR
The IQR measures the spread of the central 50% of the data. The range measures the total extent from minimum to maximum. The lower fence (Q1 − 1.5×IQR) and upper fence (Q3 + 1.5×IQR) are Tukey's outlier thresholds. Values below the lower fence or above the upper fence are plotted as individual points (outliers) on a boxplot, while the whiskers extend only to the most extreme non-outlier values.
How to use the Five-Number Summary Calculator
- 1
Enter your minimum
- 2
Enter your q1 (25th percentile)
- 3
Enter your median (q2)
- 4
Enter your q3 (75th percentile)
- 5
Enter your maximum
- 6
Read your results instantly
Results update in real time as you type.
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The five-number summary and what each component tells you
The five-number summary — minimum, Q1, median, Q3, maximum — captures the full shape of a distribution without assuming any particular form. The minimum and maximum show the total range. Q1 and Q3 bracket the central half of the data. The median shows the central value without being affected by outliers.
For the defaults (5, 15, 25, 35, 50), the IQR is 20 and the range is 45. The gap between Q3 and the maximum (15 units) is larger than the gap between the minimum and Q1 (10 units), suggesting a slight right skew — the upper tail extends further than the lower tail.
Boxplots and data visualization
The five-number summary is the foundation of a boxplot (box-and-whisker plot). The box spans from Q1 to Q3, with a line at the median. The whiskers extend to the most extreme non-outlier values (within 1.5×IQR of the quartiles). Points beyond the fences are plotted individually.
Boxplots are excellent for comparing distributions across groups — side-by-side boxplots immediately show differences in center, spread, and skewness. They are a standard tool in exploratory data analysis.
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Skewness from the five-number summary
You can infer the direction of skew from the five-number summary without computing any additional statistics. If the median is closer to Q1 than Q3, the distribution is right-skewed (long upper tail). If the median is closer to Q3, the distribution is left-skewed. If the median is centered between Q1 and Q3, the data is roughly symmetric.
Similarly, comparing the lengths of the upper whisker (Q3 to max) and lower whisker (min to Q1) indicates asymmetry in the tails. A longer upper whisker suggests a heavier right tail.
Tips & Insights
Median is more robust than mean for skewed data
The five-number summary uses the median (Q2) rather than the mean. The median is unaffected by extreme values, making it a better measure of center for skewed distributions like income or property prices.
Different software may give different quartile values
There are multiple methods for computing Q1 and Q3 from a dataset (inclusive vs. exclusive, linear interpolation). Different tools may produce slightly different quartiles. Always note which method your software uses.
Check that min ≤ Q1 ≤ median ≤ Q3 ≤ max
If your inputs violate this ordering, the summary is invalid. Q1 must be at or above the minimum, the median must be between Q1 and Q3, and Q3 must be at or below the maximum.
Worked Examples
Home prices in a neighborhood
IQR: $155,000. Upper fence: $662,500. The $950,000 home is above the upper fence — a statistical outlier. The distribution is right-skewed.
Student exam scores
IQR: 19. Lower fence: 36.5. Upper fence: 112.5. No outliers in either direction. The distribution is slightly left-skewed (median closer to Q3).
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Frequently Asked Questions
What is a five-number summary?
The five-number summary consists of the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. It provides a complete description of a dataset's distribution without assuming any particular shape.
How is the five-number summary used in boxplots?
A boxplot draws a box from Q1 to Q3 with a line at the median. Whiskers extend to the most extreme non-outlier points (within 1.5×IQR of the quartiles). Points beyond the fences are shown individually as outliers.
What does IQR tell you that range does not?
Range covers the entire spread including extreme values, making it sensitive to outliers. IQR measures only the middle 50%, so it describes typical spread without being affected by the extreme values.
How can I detect skewness from the five-number summary?
If the median is closer to Q1, the distribution is right-skewed. If the median is closer to Q3, it is left-skewed. Comparing upper and lower whisker lengths reveals asymmetry in the tails.
Do I need a large dataset to use the five-number summary?
The five-number summary is meaningful for datasets of any size, but quartile estimates become more stable with larger samples. For fewer than about 10 observations, the individual data points may be more informative than quartile summaries.
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