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Statistical Analysis
Average Calculator (Mean, Median, Mode & Range)
Calculate arithmetic mean, median, mode, range, standard deviation, and sum for any dataset. Enter numbers separated by commas, spaces, or new lines.
Arithmetic Mean (Average)
21.2857
Count (n): 7 | Sum (Σx): 149
Median
19.0000
Mode
19
Range (Max - Min)
20.0000
Std. Deviation (s)
6.9213
Understanding Measures of Central Tendency & Dispersion
In statistics, an average is a single value that summarizes a larger collection of numbers. Different measures provide unique perspectives on where the data concentrates and how widely it spreads.
Core Statistical Formulations
Arithmetic Mean: x̄ = (Σ x_i) / n
Median: Middle value of numerically ordered dataset
Sample Variance: s² = Σ(x_i - x̄)² / (n - 1)
Sample Std Deviation: s = √s²
Mean vs. Median: When to Use Which
- Mean: Best for symmetric distributions without extreme outliers (e.g. height, exam test scores).
- Median: Highly resistant to skewness and outliers (e.g. household income, real estate prices, website session durations).
- Mode: The most frequently occurring score in the dataset. Ideal for categorical or discrete survey data.
Frequently Asked Questions
If two values tie for the highest frequency, the dataset is called bimodal. If three or more tie, it is multimodal. If every value appears only once, there is no mode.
Sample standard deviation uses Bessel's correction dividing by (n - 1) to provide an unbiased estimator when evaluating a representative subset. Population standard deviation divides by N.
Educational Disclaimer: Local JavaScript math execution uses IEEE-754 double precision standard.