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Statistics Calculator — Mean, Median, Mode & Std Dev
Compute summary statistics, sample variance, standard deviation, and range from dataset.
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Sample Data Set
Sample Standard Deviation Formula
Transparent mathematical methodology explained in plain English.
s = √[ Σ(x_i - x̄)² / (n - 1) ] Measures the dispersion of data points from the sample mean x̄ using Bessel correction (n - 1) in the denominator.
Variables Explained:
- s: Sample standard deviation.
- x̄: Sample mean (average).
- n: Total number of observations.
Real Project Example
Dataset: 12, 15, 18, 22, 28
Computing descriptive statistics.
Sample Project Inputs:
Data: 12, 15, 18, 22, 28
Step-by-Step Calculation:
- Count n = 5.
- Sum = 95; Mean x̄ = 95 / 5 = 19.0.
- Median = 18.
- Squared deviations: (12-19)² + (15-19)² + (18-19)² + (22-19)² + (28-19)² = 49 + 16 + 1 + 9 + 81 = 156.
- Sample variance s² = 156 / 4 = 39.0.
- Sample standard deviation s = √39 = 6.245.
Calculated Answer: Mean = 19.0, Median = 18.0, Sample Std Dev = 6.25.
Knowledge Base
Frequently Asked Questions: Statistics Calculator
Click any question below to expand quick answers, formulas, and expert tips.
When do I use sample vs. population standard deviation?
Use sample standard deviation (n - 1) when your data represents a sample drawn from a larger group. Use population standard deviation (N) only when your data encompasses the entire complete population.