Quartile Calculator
Calculate First Quartile ($Q_1$), Second Quartile ($Q_2$ Median), Third Quartile ($Q_3$), and Interquartile Range (IQR).
Calculate Dataset Quartiles & Percentiles
Enter numbers separated by commas, spaces, or lines.
Calculation Results
Calculated using linear interpolation percentile formulas: Q_1 = P_{25}, \quad Q_2 = P_{50}, \quad Q_3 = P_{75}, \quad \text{IQR} = Q_3 - Q_1
Quick Summary
The Quartile Calculator evaluates First Quartile ($Q_1$), Median ($Q_2$), Third Quartile ($Q_3$), Interquartile Range ($\text{IQR} = Q_3 - Q_1$), and Semi-IQR.
Formula Explanation
Q_1 = 25\text{th Percentile Position } \frac{1(n + 1)}{4}
Q_2 = 50\text{th Percentile Position } \frac{2(n + 1)}{4} = \text{Median}
Q_3 = 75\text{th Percentile Position } \frac{3(n + 1)}{4}How It Works
Quartiles divide an ordered dataset into four quarters containing 25% of observations each. The Quartile Calculator sorts your numbers in ascending order and computes $Q_1$, $Q_2$ (Median), $Q_3$, and Interquartile Range (IQR).
Step-by-Step Worked Example
Practical Problem: Calculate quartiles for sorted dataset: 3, 7, 8, 12, 14, 17, 19, 21, 24, 28 ($n = 10$).
- Step 1: Calculate Median ($Q_2$): Average of 5th and 6th elements: $(14 + 17) / 2 = \mathbf{15.5000}$.
- Step 2: Calculate $Q_1$ (25th percentile): $25\%$ of 10 items $\rightarrow \mathbf{8.0000}$ (or interpolated value).
- Step 3: Calculate $Q_3$ (75th percentile): $75\%$ of 10 items $\rightarrow \mathbf{21.0000}$ (or interpolated value).
- Step 4: Calculate Interquartile Range (IQR): $\text{IQR} = Q_3 - Q_1 = 21.0 - 8.0 = \mathbf{13.0000}$.
- Step 5: Interpretation: The central 50% of data points span an IQR of 13 units.
Real-World Calculation Examples
Scenario 1: 10-Item Dataset (3 to 28)
Parameters: n = 10
Result: Q1 = 8.0, Q2 = 15.5, Q3 = 21.0 (IQR 13.0).
Scenario 2: Employee Salary Quartile Bands
Parameters: Salaries $40k to $120k
Result: Q1 $55k, Q2 $72k, Q3 $95k.
Scenario 3: Standardized Test Scoring
Parameters: SAT score distribution
Result: Q1 980, Q2 1050, Q3 1220.
Scenario 4: Real Estate Housing Prices
Parameters: Home price range
Result: IQR $140,000 (Middle 50% price span).
Key Benefits of Using This Calculator
Complete 4-Quarter Breakdown
Outputs $Q_1$, $Q_2$ (Median), $Q_3$, IQR, and Semi-IQR simultaneously.
Linear Interpolation Precision
Uses standard linear interpolation to compute exact non-integer quartile positions.
Boxplot Parameter Generation
Provides exact five-number summary values needed to draw box-and-whisker plots.
100% Free & Client-Side
Executes locally in your browser with zero latency or web server transmission.
Frequently Asked Questions (FAQ)
What are quartiles in statistics?
Quartiles are values that divide a rank-ordered dataset into four equal parts (25% each).
What is $Q_1, Q_2, Q_3$?
$Q_1$ is 25th percentile (lower quartile), $Q_2$ is 50th percentile (median), and $Q_3$ is 75th percentile (upper quartile).
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 quartiles in Excel?
Use formula =QUARTILE.EXC(range, quart) or =QUARTILE.INC(range, quart).
What is difference between QUARTILE.INC and QUARTILE.EXC?
QUARTILE.INC includes 0 and 100% endpoints; QUARTILE.EXC excludes endpoints for continuous random variables.
What is semi-interquartile range?
Semi-interquartile range is $\frac{Q_3 - Q_1}{2}$.
How are quartiles used to identify outliers?
Values below $Q1 - 1.5 \times \text{IQR}$ or above $Q3 + 1.5 \times \text{IQR}$ are classified as outliers.
Can quartiles be negative numbers?
Yes — if dataset values are negative, quartiles will be negative.
What is quartile skewness coefficient (Bowley Skewness)?
Bowley skewness coefficient is $\frac{Q_1 + Q_3 - 2 Q_2}{Q_3 - Q_1}$.
What proportion of data lies between $Q_1$ and $Q_3$?
Exactly 50% of the dataset observations lie between $Q_1$ and $Q_3$.