5 Number Summary Calculator

Central Tendency and Dispersion Measures

Enter a list of numbers separated by commas to get the minimum, first quartile (Q1), median, third quartile (Q3), and maximum.

Practical Examples

See how the 5 Number Summary Calculator works with sample data sets.

Student Test Scores

Student Test Scores

A small class of 10 students' scores on a recent exam.

Data Set: 88, 92, 80, 75, 95, 85, 78, 89, 90, 81

Daily Commute Times (Minutes)

Daily Commute Times (Minutes)

Commute times recorded over two work weeks (10 days).

Data Set: 25, 30, 28, 35, 40, 22, 33, 38, 29, 31

Housing Prices ($1000s)

Housing Prices ($1000s)

A sample of 9 house prices in a neighborhood.

Data Set: 250, 275, 300, 280, 320, 290, 265, 310, 295

Employee Ages

Employee Ages

A dataset with an even number of data points representing employee ages.

Data Set: 23, 45, 33, 28, 52, 41, 38, 29, 35, 48

Other Titles
Understanding the 5 Number Summary: A Comprehensive Guide
Dive deep into one of the fundamental tools of descriptive statistics to understand your data's distribution and central tendency.

What is the 5 Number Summary?

  • Core Components
  • The Role of Quartiles
  • Why It's Important
The 5 number summary is a set of descriptive statistics that provides a concise overview of the distribution of a dataset. It consists of five key values: the minimum, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum. This summary is highly effective for quickly gauging the center, spread, and skewness of your data.
Core Components Explained
Minimum (Min): The smallest value in the dataset. It represents the lower boundary of your data.
First Quartile (Q1): Also known as the 25th percentile. 25% of the data falls below this value.
Median (Q2): The middle value of the dataset (the 50th percentile). It separates the data into two equal halves.
Third Quartile (Q3): The 75th percentile. 75% of the data falls below this value.
Maximum (Max): The largest value in the dataset, representing the upper boundary.

Conceptual Example

  • For the dataset [1, 2, 5, 7, 10], the minimum is 1 and the maximum is 10.
  • The median of [1, 2, 5, 7, 10] is 5, the middle number.

Step-by-Step Guide to Using the Calculator

  • Data Entry
  • Interpreting the Results
  • Using the Advanced Metrics
Using our calculator is straightforward. First, gather your numerical data. Ensure the numbers are clean and ready for analysis.
1. Enter Your Data
Type or paste your numbers into the 'Data Set' input field. The numbers must be separated by commas. Any non-numeric characters or extra spaces will be automatically handled by the calculator.
2. Calculate and Review
Click the 'Calculate' button. The tool will instantly display the 5 number summary results, along with other useful statistics like the Interquartile Range (IQR), mean, and standard deviation.

Input Examples

  • Valid Input: 10, 20, 30, 40, 50
  • Input with extra spaces: 5, 15, 25, 35

Real-World Applications of the 5 Number Summary

  • Financial Analysis
  • Educational Assessment
  • Scientific Research
The 5 number summary is not just an academic concept; it has numerous practical applications across various fields.
Box Plots and Data Visualization
The primary application is in the creation of box plots (or box-and-whisker plots). A box plot is a visual representation of the 5 number summary, making it incredibly easy to compare distributions between different groups.
Identifying Skewness and Outliers
By examining the distance between the components, you can infer the data's skewness. For instance, if the median is closer to Q1, the data is likely skewed right. The Interquartile Range (IQR) is also crucial for identifying potential outliers in the dataset.

Application Scenarios

  • Comparing test scores between two different schools to see which has a better overall performance and consistency.
  • Analyzing housing prices in a city to understand the market's spread and central price point.

Calculation Methods and Formulas

  • Ordering the Data
  • Finding the Median
  • Calculating Quartiles
Understanding how the summary is calculated can help you interpret the results more effectively. The process is systematic and follows a clear set of rules.
The Quartile Calculation Method
There are several methods for calculating quartiles. This calculator uses the Tukey method (also known as the inclusive method). After finding the median (Q2), the dataset is split into two halves. If the number of data points (n) is odd, the median is included in both halves. Q1 is the median of the lower half, and Q3 is the median of the upper half.
Interquartile Range (IQR)
The IQR is a measure of statistical dispersion and is calculated as the difference between the third and first quartiles: IQR = Q3 - Q1. It represents the range where the middle 50% of your data lies.

Calculation Walkthrough

  • Data: [2, 4, 4, 5, 6, 7, 8]. n=7 (odd). Median is 5. Lower half: [2, 4, 4, 5]. Q1 is (4+4)/2 = 4. Upper half: [5, 6, 7, 8]. Q3 is (6+7)/2 = 6.5.
  • Data: [1, 2, 3, 4, 5, 6]. n=6 (even). Median is (3+4)/2 = 3.5. Lower half: [1, 2, 3]. Q1 is 2. Upper half: [4, 5, 6]. Q3 is 5.