Descriptive Statistics Calculator
Comprehensive Statistical Analysis
Get complete descriptive statistics including:
- Central Tendency: Mean, median, mode
- Dispersion: Standard deviation, variance, IQR
- Shape: Skewness and kurtosis
- Five-Number Summary: Min, Q1, Q2, Q3, Max
- Outlier Detection: Using 1.5×IQR method
- Coefficient of Variation: Relative variability
Perfect for: Complete data analysis and statistical reporting
Perform comprehensive descriptive statistical analysis with advanced metrics including quartiles, skewness, kurtosis, and detailed data summaries.
What are Descriptive Statistics?
Descriptive statistics provide comprehensive summaries and descriptions of datasets, including measures of central tendency, dispersion, and shape.
Complete Statistical Summary
Central Tendency
Mean: Arithmetic average
Median: Middle value
Mode: Most frequent value
Trimmed Mean: Mean excluding outliers
Dispersion
Range: Max - Min
IQR: Q3 - Q1
Variance: Squared deviations
Standard Deviation: √Variance
Advanced Descriptive Measures
| Statistic | What It Measures | Interpretation | Normal Range |
|---|---|---|---|
| Skewness | Distribution asymmetry | Direction of tail | -2 to +2 |
| Kurtosis | Distribution peakedness | Tail heaviness | Around 3 |
| Coefficient of Variation | Relative variability | Standardized spread | 0% to 100%+ |
Five-Number Summary
The five-number summary provides a complete picture of data distribution:
- Minimum: Smallest value
- Q1 (First Quartile): 25th percentile
- Q2 (Median): 50th percentile
- Q3 (Third Quartile): 75th percentile
- Maximum: Largest value
Box Plot: The five-number summary is used to create box-and-whisker plots for visual data analysis.
Applications
Research
- Survey data analysis
- Experimental results
- Clinical trial outcomes
- Behavioral studies
Business
- Sales performance analysis
- Customer satisfaction
- Market research
- Quality control
Education
- Test score analysis
- Grade distribution
- Student performance
- Assessment evaluation
Statistical Shape Measures
- Symmetric Distribution: Mean = Median, Skewness ≈ 0
- Right Skewed: Mean > Median, Positive skewness
- Left Skewed: Mean < Median, Negative skewness
- Normal Distribution: Symmetric, Kurtosis ≈ 3
- Heavy Tails: Kurtosis > 3 (leptokurtic)
- Light Tails: Kurtosis < 3 (platykurtic)
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