Key Statistical Measures Explained
- Mean (Average): Sum of all values ÷ count. Sensitive to outliers. Best for normally distributed data.
- Median: Middle value when sorted. Robust to outliers. Better for skewed distributions (e.g., income data).
- Mode: Most frequently occurring value. Useful for categorical data.
- Standard Deviation: Measures how spread out values are from the mean. Low SD = data clustered tightly; high SD = widely spread.
- Variance: Standard deviation squared. Useful in statistical formulas but less intuitive as a standalone measure.
- Range: Max minus Min. Quick measure of spread but sensitive to outliers.
Population vs Sample Statistics
Our calculator uses population standard deviation (divide by N), which is correct when your dataset represents the entire population. If your data is a sample from a larger population, use the sample standard deviation (divide by N−1) for an unbiased estimate. The difference is negligible for large datasets (N > 30) but matters for small samples.
Standard Deviation FormulasPopulation σ = √[Σ(x − μ)² ÷ N]
Sample s = √[Σ(x − x̄)² ÷ (N−1)]
Sample s = √[Σ(x − x̄)² ÷ (N−1)]
Example Calculation
Dataset: [4, 7, 13, 2, 9, 15, 7, 3]
| Measure | Value |
|---|---|
| Count (N) | 8 |
| Sum | 60 |
| Mean | 7.5 |
| Median | 7.0 |
| Mode | 7 |
| Std Dev (pop) | 4.36 |
| Variance | 19.0 |
| Range | 13 (2 to 15) |
📉 Analyse any dataset — paste numbers, get full stats instantly
Open Statistics Calculator →statistics calculatormean median mode calculatorstandard deviation calculatorvariance calculatordescriptive statisticsaverage calculatorstatistical analysis