📊 5 Number Summary Calculator

What is the 5 Number Summary?

The five number summary is a set of descriptive statistics that provides a comprehensive overview of a dataset's distribution. It consists of five key values: the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. These values divide the dataset into four equal parts, each containing 25% of the data points.

Components of the Five Number Summary

How to Find 5 Number Summary

Finding the five number summary manually involves these steps:

1. Sort your data in ascending order (smallest to largest)
2. Identify the minimum (first number) and maximum (last number)
3. Find the median by locating the middle value
4. Split the data into lower and upper halves (excluding median if odd count)
5. Calculate Q1 as the median of the lower half
6. Calculate Q3 as the median of the upper half
7. Optionally calculate IQR = Q3 - Q1 for spread analysis

Uses of the 5 Number Summary

• Creating Box Plots: The five numbers form the foundation of box-and-whisker plots
• Identifying Outliers: Values beyond Q1 - 1.5×IQR or Q3 + 1.5×IQR are potential outliers
• Comparing Datasets: Quickly compare distributions of different groups
• Understanding Spread: IQR shows the spread of the middle 50% of data
• Data Analysis: Essential in exploratory data analysis and descriptive statistics
• Quality Control: Monitor process variation and identify unusual values

Quartile Calculation Methods

There are different methods for calculating quartiles. Our calculator uses the inclusive method (method used by most statistics textbooks):

Practical Applications

• Education: Analyze test scores and grade distributions
• Business: Understand salary ranges and sales performance
• Healthcare: Study patient vital signs and treatment outcomes
• Sports: Analyze player statistics and performance metrics
• Research: Summarize experimental data and survey results
• Finance: Assess investment returns and risk metrics