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📊 Average Calculator

Calculate mean, median, mode, range, standard deviation, variance, geometric & harmonic mean and more — with step-by-step solutions.

Enter Numbers
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Parsed Numbers
Weighted Average
ValueWeight
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Weighted Average
Percentile Lookup
Find percentile:
th
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Percentile Value
Common Percentiles
Running Stats
Calculate to see running stats
Formula Reference
Mean = Σx / n
Median = middle value of sorted set
Mode = most frequent value(s)
Range = max − min
Variance (pop) = Σ(x−μ)² / n
Std Dev (pop) = √Variance
Geo Mean = (∏x)^(1/n)
Harm Mean = n / Σ(1/x)
IQR = Q3 − Q1
CV = (Std Dev / Mean) × 100%

About Statistical Averages

Mean vs Median

The arithmetic mean (average) is sensitive to outliers — a single extreme value can skew it dramatically. The median (middle value) is robust to outliers and better represents the "typical" value in skewed distributions like income data.

Standard Deviation

Standard deviation measures the spread of numbers around the mean. A low SD means values are clustered closely; a high SD means they are spread out. Population SD divides by n; sample SD divides by (n−1) to correct for estimation bias.

Geometric Mean

The geometric mean is ideal for averaging rates of change, ratios, or percentages (like investment returns). It is calculated as the nth root of the product of all values. All values must be positive for a real result.

Weighted Average

A weighted average assigns different levels of importance to each value. Common uses include GPA calculation (credit hours as weights), price indices, and survey responses. Formula: Σ(value × weight) / Σweight.