Quartiles and Percentiles Calculator
Results:
Understanding Quartiles and Percentiles
What are Quartiles and Percentiles?
Quartiles and percentiles are measures that divide a dataset into equal parts:
- Quartiles divide data into four equal parts (25% each)
- Percentiles divide data into 100 equal parts (1% each)
- Q1 (25th percentile): First quartile
- Q2 (50th percentile): Median
- Q3 (75th percentile): Third quartile
- IQR = Q3 - Q1: Interquartile Range
Calculation Methods
Method 1: Linear Interpolation
Uses position = (n+1)p where p is the desired percentile
Method 2: Nearest Rank
Uses position = ceil(np) where n is sample size
Method 3: Empirical Distribution
Uses position = np rounded to nearest integer
Important Properties
- Quartiles are special cases of percentiles
- Q2 (median) equals P50
- IQR contains middle 50% of data
- Outliers: < Q1 - 1.5×IQR or > Q3 + 1.5×IQR
- Robust to extreme values
Applications and Uses
- Data Distribution Analysis:
- Shape and spread of data
- Identifying outliers
- Comparing distributions
- Statistical Process Control:
- Quality control limits
- Process capability
- Performance metrics
- Educational Assessment:
- Standardized test scores
- Grade distributions
- Performance rankings
Box Plot Components
| Component | Description | Interpretation |
|---|---|---|
| Minimum | Smallest non-outlier | Lower boundary |
| Q1 (25th) | First quartile | Lower box edge |
| Median | Middle value | Center line |
| Q3 (75th) | Third quartile | Upper box edge |
| Maximum | Largest non-outlier | Upper boundary |
Advanced Concepts
Skewness
Asymmetry in data distribution relative to quartiles
Outlier Detection
Using IQR method for identifying unusual values
Robust Statistics
Resistance to extreme values and outliers
Real-World Applications
Finance
Risk assessment and portfolio analysis
Healthcare
Patient outcomes and diagnostic ranges
Education
Test scores and performance metrics
Manufacturing
Quality control and process monitoring