Average Calculator
Calculate mean, median, mode, variance, standard deviation, percentiles, trimmed and weighted averages. Paste numbers, upload CSV or type value:weight pairs.
How this Average Calculator Works — Detailed
This tool supports raw lists and value:weight pairs. It uses real calendar-safe numeric math (no external libs). Below are definitions, formulas, examples and guidance so the output is useful and defensible.
Definitions & formulas
- Mean (arithmetic): sum(x_i) / n
- Weighted mean: sum(w_i * x_i) / sum(w_i)
- Median: middle value of sorted list (or average of two middles)
- Mode: most frequent value(s). This tool reports all modes.
- Variance: population: sum((x-μ)^2)/n; sample: sum((x-μ)^2)/(n-1)
- Std dev: square root of variance (sample/population selectable)
- Geometric mean: (Π x_i)^(1/n) — only for positive numbers
- Harmonic mean: n / sum(1/x_i) — only for non-zero numbers
- Trimmed mean: remove p% lowest and p% highest values then compute mean
- Percentiles: computed by linear interpolation on sorted values
Examples
- Data: 2, 4, 4, 4, 5, 5, 7 → mean ≈ 4.43, median = 4, mode = 4
- Weighted: 90:0.2, 80:0.5, 70:0.3 → weighted mean = (90*0.2+80*0.5+70*0.3) / (0.2+0.5+0.3) = 80
- Trim 10% from each end removes 10% low & high values before averaging (useful when outliers distort the mean)
When to use each metric
Mean for symmetric distributions, median for skewed data, trimmed mean when a few extreme values bias the mean, weighted mean when observations differ in importance. Use sample std dev for statistical inference; use population std dev when you have the entire population.
Frequently Asked Questions
The parser ignores empty entries and non-numeric tokens. For value:weight pairs use colon (:) to separate. When upload CSV with two columns the second column is treated as weight if 'Use weighted pairs' is checked.
Negative numbers and zero are accepted for arithmetic mean, median, mode, variance and std dev. Geometric mean requires strictly positive values; harmonic mean excludes zeros.
If multiple values tie for highest frequency, all are shown as modes. If all values are unique, the mode is 'none'.
Yes — click Download CSV to get a one-line CSV with the main metrics and another CSV format of cleaned input values if required.
Std dev describes dispersion of data around the mean. About 68% of data lie within ±1σ for roughly normal distributions. Use sample std dev (n-1) for estimates from a sample.