Five Number Summary Calculator
Calculate five-number summary $[\text{Min}, Q_1, \text{Median } Q_2, Q_3, \text{Max}]$, Interquartile Range (IQR), and boxplot parameters for any dataset.
Calculate Five-Number Summary & Boxplot Parameters
Enter numbers separated by commas, spaces, or lines.
Calculation Results
Calculated using five-number summary statistical standards: \text{Summary} = [\text{Min}, Q_1, Q_2 (\text{Median}), Q_3, \text{Max}]
Quick Summary
The Five Number Summary Calculator evaluates Minimum, First Quartile ($Q_1$), Median ($Q_2$), Third Quartile ($Q_3$), and Maximum ($\text{Max}$).
Formula Explanation
\text{Five-Number Summary} = [\text{Min}, Q_1, \text{Median } Q_2, Q_3, \text{Max}]
\text{IQR} = Q_3 - Q_1How It Works
The five-number summary provides a concise five-point snapshot of dataset distribution. The Five Number Summary Calculator sorts your data into ascending order, identifying the minimum, $Q_1$ (25th percentile), median ($Q_2$), $Q_3$ (75th percentile), and maximum.
Step-by-Step Worked Example
Practical Problem: Calculate five-number summary for dataset: 4, 11, 15, 20, 24, 28, 33, 37, 42 ($n = 9$).
- Step 1: Identify Minimum ($\text{Min}$): $\text{Min} = \mathbf{4.0000}$.
- Step 2: Calculate First Quartile ($Q_1$): 25th percentile value $= \mathbf{15.0000}$.
- Step 3: Calculate Median ($Q_2$): Middle 5th element $= \mathbf{24.0000}$.
- Step 4: Calculate Third Quartile ($Q_3$): 75th percentile value $= \mathbf{33.0000}$.
- Step 5: Identify Maximum ($\text{Max}$): $\text{Max} = \mathbf{42.0000}$. Five-number summary $= \mathbf{[4, 15, 24, 33, 42]}$.
Real-World Calculation Examples
Scenario 1: 9-Item Dataset (4 to 42)
Parameters: n = 9
Result: [4, 15, 24, 33, 42] (IQR = 18).
Scenario 2: Student Exam Grade Summary
Parameters: Min 45, Q1 65, Q2 78, Q3 88, Max 98
Result: [45, 65, 78, 88, 98].
Scenario 3: Corporate Employee Age Distribution
Parameters: Min 22, Q1 30, Q2 38, Q3 48, Max 65
Result: [22, 30, 38, 48, 65].
Scenario 4: Box Plot Whisker Construction
Parameters: Five-number summary parameters
Result: Direct input for boxplot drawing.
Key Benefits of Using This Calculator
Complete Boxplot Data Profile
Generates all five essential statistical values needed for box-and-whisker plot construction.
Interquartile Range (IQR) Included
Calculates Interquartile Range ($\text{IQR} = Q_3 - Q_1$) alongside the five-number summary.
Non-Parametric Analysis
Provides a non-parametric summary independent of underlying normal distribution assumptions.
100% Free & Client-Side
Executes locally in your browser with zero latency or web server transmission.
Frequently Asked Questions (FAQ)
What is a five-number summary?
The five-number summary consists of the five key descriptive statistics: Minimum, First Quartile ($Q_1$), Median ($Q_2$), Third Quartile ($Q_3$), and Maximum.
How is five-number summary used in a box plot?
The box spans from $Q_1$ to $Q_3$, a line inside marks the Median ($Q_2$), and whiskers extend to Minimum and Maximum (or non-outlier fences).
What is Interquartile Range (IQR)?
IQR is the difference between $Q_3$ and $Q_1$ ($\text{IQR} = Q_3 - Q_1$).
How do I calculate five-number summary in Excel?
Use functions =MIN(), =QUARTILE(1), =MEDIAN(), =QUARTILE(3), and =MAX().
Can five-number summary be calculated for small datasets ($n < 5$)?
Yes — linear interpolation calculates five-number summary for datasets with fewer than 5 observations.
What does asymmetry in a five-number summary indicate?
If $\text{Median} - Q_1 \neq Q_3 - \text{Median}$, the dataset distribution is skewed.
Who invented the five-number summary and box plot?
American statistician John Tukey introduced the five-number summary and box-and-whisker plot in 1970.
Can five-number summary values be negative?
Yes — negative values are fully supported in five-number summary calculations.
What is six-number summary?
A six-number summary adds the arithmetic mean ($\bar{x}$) to the five-number summary.
What is midhinge?
Midhinge is the average of $Q_1$ and $Q_3$ ($\text{Midhinge} = \frac{Q_1 + Q_3}{2}$).