Five-Number Summary Calculator
Produce the five-number summary (min, Q1, median, Q3, max) from sorted data values.
IQR
30.0000
IQR vs Minimum
公式
## Five-Number Summary ### Components 1. **Minimum**: Smallest observation 2. **Q1**: First quartile (25th percentile) 3. **Median**: Middle value (50th percentile) 4. **Q3**: Third quartile (75th percentile) 5. **Maximum**: Largest observation These five values provide a quick sketch of the data distribution and form the basis for box-and-whisker plots. The whisker fences at Q1 - 1.5*IQR and Q3 + 1.5*IQR mark the boundary for potential outliers.
计算示例
A dataset has min=5, Q1=15, median=30, Q3=45, max=80.
- 01Five-Number Summary: 5, 15, 30, 45, 80
- 02Range = 80 - 5 = 75
- 03IQR = 45 - 15 = 30
- 04Lower Fence = 15 - 1.5*30 = 15 - 45 = -30
- 05Upper Fence = 45 + 1.5*30 = 45 + 45 = 90
常见问题
What is the five-number summary used for?
It summarizes the distribution with just five values and is the foundation for constructing box plots, which visually show center, spread, and skewness.
How can I tell if data is skewed from the five-number summary?
Compare the distances: if (Median - Min) >> (Max - Median), the data is left-skewed. If (Max - Median) >> (Median - Min), it is right-skewed. Also compare Q3 - Median vs. Median - Q1.
What if a value lies beyond the whisker fences?
Points beyond the fences are potential outliers. They are typically plotted as individual dots beyond the whiskers in a box plot.
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