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

9
Minimum
21.5
Q1
30
Median
39
Q3
48
Maximum

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

1

Minimum

Smallest value in the dataset

2

First Quartile (Q1)

25% of data falls below this value

3

Median (Q2)

Middle value; 50% below, 50% above

4

Third Quartile (Q3)

75% of data falls below this value

5

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