Quartile Calculator
What is a Quartile Calculator?
A quartile calculator is a statistical tool that divides a dataset into four equal parts, helping you understand the distribution of your data. Quartiles are values that divide your ordered dataset into quarters, with each quarter containing 25% of the data points.
The three quartiles are:
- Q₁ (First Quartile): The median of the lower half of the data (25th percentile)
- Q₂ (Second Quartile): The median of the entire dataset (50th percentile)
- Q₃ (Third Quartile): The median of the upper half of the data (75th percentile)
The Interquartile Range (IQR) is calculated as Q₃ - Q₁ and represents the range containing the middle 50% of your data, making it useful for identifying outliers and understanding data spread.
How It Works
Enter Data
Input your dataset separated by commas or spaces
Auto Sort
Data is automatically sorted in ascending order
Calculate
Q₁, Q₂, Q₃, and IQR are computed instantly
Common Examples
Example 1: Test Scores
Data: 65, 70, 75, 80, 85, 90, 95
Q₁: 70 (25% scored below this)
Q₂: 80 (median score)
Q₃: 90 (75% scored below this)
IQR: 20 (middle 50% range)
Example 2: Sales Data
Data: 100, 150, 200, 250, 300, 350, 400, 450, 500
Q₁: 175 (lower quartile)
Q₂: 300 (median)
Q₃: 425 (upper quartile)
IQR: 250 (interquartile range)
Calculation Table
| Quartile | Formula | Position | Description |
|---|---|---|---|
| Q₁ | (n+1)/4 | 25th percentile | First quartile, lower quartile |
| Q₂ | (n+1)/2 | 50th percentile | Second quartile, median |
| Q₃ | 3(n+1)/4 | 75th percentile | Third quartile, upper quartile |
| IQR | Q₃ - Q₁ | Middle 50% | Interquartile range |
Note: When the position is not a whole number, interpolation is used between adjacent values.
Frequently Asked Questions
What are quartiles and how are they calculated?
Quartiles divide a sorted dataset into four equal parts. Q₁ is at position (n+1)/4, Q₂ (median) at (n+1)/2, and Q₃ at 3(n+1)/4. When positions aren't whole numbers, we interpolate between adjacent values.
What is the Interquartile Range (IQR)?
IQR = Q₃ - Q₁ represents the range containing the middle 50% of your data. It's useful for identifying outliers and understanding data spread, as it's less affected by extreme values than the full range.
How do I input my data?
Enter your numbers separated by commas or spaces. For example: "1, 2, 3, 4, 5" or "1 2 3 4 5". The calculator will automatically sort your data and compute all quartiles.
When should I use quartiles?
Quartiles are useful for analyzing data distribution, identifying outliers, creating box plots, comparing datasets, and understanding where specific values fall within your data range. They're commonly used in statistics, research, and data analysis.
Is this calculator accurate?
Yes, this calculator uses the standard quartile calculation method with linear interpolation for non-integer positions. It follows the same formulas used in statistical software and textbooks, providing accurate results for any dataset size.