Five-Number Summary Calculator
Generate the five-number summary (minimum, Q1, median, Q3, maximum) for any dataset. Calculate IQR, range, mean, standard deviation, detect outliers using Tukey's fences, and visualize data with an interactive box plot.
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Five-Number Summary Calculator - Box Plot Statistics
Calculate the five-number summary including minimum, first quartile (Q1), median, third quartile (Q3), and maximum. Generate box plots, detect outliers with Tukey's fences, and analyze your data distribution with step-by-step calculations.
What is a Five-Number Summary?
The five-number summary is a set of descriptive statistics that provides a concise overview of a dataset's distribution. It consists of: the minimum (smallest value), first quartile Q1 (25th percentile), median Q2 (50th percentile), third quartile Q3 (75th percentile), and maximum (largest value). These five values divide the data into four equal parts and form the basis for box plot visualization, making it easy to identify spread, skewness, and potential outliers.
Five-Number Summary Components
Min, Q₁, Median (Q₂), Q₃, MaxHow to Calculate a Five-Number Summary
Applications of Five-Number Summary
Exploratory Data Analysis
Quickly understand data distribution, identify spread, and detect potential outliers before deeper analysis.
Comparing Distributions
Use side-by-side box plots to compare multiple groups, such as test scores across classes or sales across regions.
Quality Control
Monitor process variation and detect unusual values in manufacturing or service delivery metrics.
Research and Academia
Report descriptive statistics for non-normal data in scientific papers and statistical reports.
Frequently Asked Questions
The exclusive method (TI-83 style) excludes the median when calculating Q1 and Q3, dividing the data into upper and lower halves without including the median in either half. The inclusive method (Tukey's hinges) includes the median in both halves when the dataset has an odd number of values. Both methods are valid; exclusive is common in statistics software and calculators, while inclusive follows Tukey's original definition.