Descriptive Statistics Calculator
Calculate comprehensive descriptive statistics including central tendency, dispersion, and distribution shape
Calculate Descriptive Statistics
Sample data represents a subset; population data represents the entire group
You can enter up to 1000 values. At least 2 values are required for meaningful statistics.
What are Descriptive Statistics?
Summarize and describe key features of datasets
Measure central tendency (mean, median, mode)
Assess variability and dispersion
Identify outliers and distribution shape
Provide foundation for inferential statistics
Key Statistical Measures
Central Tendency
Mean, median, mode, midrange
Dispersion
Variance, standard deviation, range, IQR
Position
Quartiles, percentiles, five-number summary
Shape
Skewness, kurtosis
Outliers
Fences, outlier identification
Sample vs Population
Sample Data
Subset of the population
Uses n-1 for variance calculation (Bessel's correction)
Population Data
Complete dataset
Uses n for variance calculation
Tip: Use "Sample" for most real-world data analysis scenarios
Understanding Descriptive Statistics
What are Descriptive Statistics?
Descriptive statistics are numerical summaries that describe the main features of a dataset. They provide simple summaries about the sample and the measures, forming the basis of virtually every quantitative analysis of data.
Categories of Descriptive Statistics
- •Central Tendency: Where the data clusters (mean, median, mode)
- •Variability: How spread out the data is (variance, standard deviation)
- •Distribution: The shape of the data (skewness, kurtosis)
Interpretation Guidelines
Skewness Interpretation
- |Skew| < 0.5: Approximately symmetric
- Skew > 0.5: Positively skewed (right tail)
- Skew < -0.5: Negatively skewed (left tail)
Kurtosis Interpretation
- |Kurt| < 0.5: Mesokurtic (normal-like)
- Kurt > 0.5: Leptokurtic (heavy tails)
- Kurt < -0.5: Platykurtic (light tails)
Practical Applications
Quality Control
Monitor process variation and identify out-of-control conditions
Market Research
Understand customer behavior patterns and preferences
Academic Assessment
Analyze test scores and grade distributions