Dispersion Calculator
Calculate measures of dispersion to understand the spread and variability of your data
Calculate Statistical Dispersion
Select whether your data represents a sample or entire population
Enter at least 2 values. Separate values with commas, spaces, semicolons, or new lines.
Example Calculation
Sample Data: Student Test Scores
Data values: 85, 88, 92, 78, 95, 82, 90, 87, 91, 89
Sample size (n): 10
Data type: Sample
Key Results
Mean: 87.7
Standard Deviation: 4.97
Variance: 24.68
Range: 17 (95 - 78)
IQR: 6.25 (90.25 - 84)
Dispersion Measures
Standard Deviation
Most common measure
Shows average distance from mean
Variance
Square of standard deviation
Measures variability
Range
Max - Min
Simple spread measure
Interquartile Range
Q3 - Q1
Middle 50% spread
Interpretation Tips
Higher values indicate more spread out data
Standard deviation is in same units as data
IQR is resistant to outliers
Use sample formula (n-1) for sample data
Understanding Statistical Dispersion
What is Dispersion?
Statistical dispersion measures how spread out or scattered data points are around the central tendency (mean, median). It tells you whether data points are clustered closely together or spread across a wide range.
Why Calculate Dispersion?
- •Understand data variability and reliability
- •Compare spread between different datasets
- •Identify outliers and data quality issues
- •Make informed decisions based on data consistency
Key Formulas
Variance
Population: σ² = Σ(x - μ)² / N
Sample: s² = Σ(x - x̄)² / (n - 1)
Standard Deviation
σ = √(variance)
Range & IQR
Range = Max - Min
IQR = Q3 - Q1