Statistics Calculator
Comprehensive statistical analysis including descriptive statistics, distribution analysis, outlier detection, and data visualization.
Comprehensive Statistics Calculator
Complete Statistical Analysis
Dataset (15 values)
[12, 15, 18, 20, 22, 25, 28, 30, 32, 35, 38, 40, 42, 45, 48]
Mean
30.000
Average value
Median
30.000
Middle value
Mode
None
Most frequent
Range
36.000
12.0 to 48.0
Std Dev (Pop)
10.869
Population
Std Dev (Sample)
11.250
Sample
Five Number Summary
Minimum: 12.000
Q1 (25th percentile): 20.000
Median (50th percentile): 30.000
Q3 (75th percentile): 40.000
Maximum: 48.000
IQR: 20.000
Variability Measures
Population Variance: 118.1333
Sample Variance: 126.5714
Coefficient of Variation: 36.23%
Outliers Detected: 0
Powered by Free-Calculator.com
What is Statistics Calculator?
This comprehensive statistics calculator provides complete descriptive statistical analysis of your dataset. It calculates all major statistical measures including central tendency, variability, distribution shape, and outlier detection with detailed interpretations and visualizations.
Descriptive Statistics Covered
- Central Tendency: Mean, median, and mode to show typical values
- Variability: Range, variance, standard deviation, and IQR
- Position: Quartiles, percentiles, and five-number summary
- Shape: Skewness and kurtosis to describe distribution form
- Outliers: Detection using the 1.5 × IQR rule
Understanding Your Results
- Mean vs Median: Compare to understand distribution symmetry
- Standard Deviation: Lower values indicate data clustering around the mean
- Coefficient of Variation: Relative variability as a percentage
- Skewness: Positive = right tail, negative = left tail, near zero = symmetric
- IQR: Contains the middle 50% of your data
Practical Applications
- Quality Control: Monitor process consistency and identify defects
- Academic Research: Analyze experimental data and survey results
- Business Analytics: Understand customer behavior, sales patterns
- Healthcare: Analyze patient data, treatment outcomes
- Finance: Risk assessment, portfolio analysis, market research
Interpreting Distributions
- Symmetric: Mean ≈ Median, low skewness
- Right-skewed: Mean > Median, positive skewness
- Left-skewed: Mean < Median, negative skewness
- Normal-like: Kurtosis near 0, symmetric shape
FAQ - Statistics Calculator
Population statistics describe the entire group you're studying (divide by N for variance). Sample statistics describe a subset representing a larger population (divide by N-1 for variance). Use sample statistics when your data represents part of a larger group.