5 Number Summary Calculator
Calculate the five-number summary: minimum, Q1, median, Q3, and maximum
Enter Your Data
Enter up to 30 numbers separated by commas or spaces
Example: Test Scores Analysis
Student Test Scores (out of 50)
Raw Scores: 32, 21, 38, 12, 44, 42, 37, 36, 21, 9, 40, 33, 22, 25, 27, 29, 30, 48, 19, 17, 30, 22, 45, 42
Sample Size: 24 students
Calculated 5-Number Summary
Interpretation: Most students scored above 21.5 points, with half scoring above 30 points. The median of 30 indicates generally good performance.
5-Number Summary Components
Minimum
Smallest value in the dataset
First Quartile (Q1)
25% of data falls below this value
Median (Q2)
Middle value; 50% below, 50% above
Third Quartile (Q3)
75% of data falls below this value
Maximum
Largest value in the dataset
Key Insights
IQR (Q3-Q1) measures data spread
Median is less affected by outliers than mean
Box plots visualize the 5-number summary
Values beyond fences are potential outliers
Understanding the 5-Number Summary
What is the 5-Number Summary?
The 5-number summary is a set of descriptive statistics that provides a comprehensive overview of a dataset's distribution. It consists of five key values: minimum, first quartile (Q1), median, third quartile (Q3), and maximum.
Why Use It?
- •Provides more information than just the average
- •Shows data distribution and spread
- •Identifies potential outliers
- •Forms the basis for box plots
Calculation Methods
Quartile Formulas:
- Q1 Position: (n+1)/4
- Median Position: (n+1)/2
- Q3 Position: 3(n+1)/4
Outlier Detection
- Lower Fence: Q1 - 1.5 × IQR
- Upper Fence: Q3 + 1.5 × IQR
- Outliers: Values beyond fences