Mean Calculator
Calculate the arithmetic, geometric, harmonic, and weighted mean of a data set. See also Median Calculator and Standard Deviation Calculator.
How to Calculate the Mean
The mean (average) is the most common measure of central tendency. To calculate the arithmetic mean, add all values in the data set and divide by the number of values. The geometric mean multiplies all values and takes the nth root, while the harmonic mean divides the count by the sum of reciprocals. Each type of mean is suited for different types of data and analysis.
Mean Formulas
Arithmetic Mean = (x₁ + x₂ + ... + xₙ) / n
Geometric Mean = (x₁ × x₂ × ... × xₙ)^(1/n)
Harmonic Mean = n / (1/x₁ + 1/x₂ + ... + 1/xₙ)
Weighted Mean = Σ(wᵢ × xᵢ) / Σwᵢ
Example Calculation
Data: 10, 20, 30, 40, 50
Sum = 10 + 20 + 30 + 40 + 50 = 150
Count = 5
Arithmetic Mean = 150 / 5 = 30
Geometric Mean = (10 × 20 × 30 × 40 × 50)^(1/5) ≈ 26.051711
Harmonic Mean = 5 / (1/10 + 1/20 + 1/30 + 1/40 + 1/50) ≈ 21.897811
Comparison of Mean Types
| Type | Best For | Sensitive to Outliers? |
|---|---|---|
| Arithmetic Mean | General-purpose average | Yes |
| Geometric Mean | Growth rates, ratios | Less so |
| Harmonic Mean | Rates, speeds | Less so |
| Weighted Mean | Unequal importance values | Depends on weights |
Frequently Asked Questions
What is the difference between mean and average?
In everyday language, "average" and "mean" are used interchangeably. Technically, "average" can refer to mean, median, or mode, but "mean" specifically refers to the arithmetic mean — the sum divided by the count.
When should I use geometric mean instead of arithmetic mean?
Use geometric mean when dealing with percentages, growth rates, or ratios. For example, average investment returns over multiple years should use geometric mean because returns compound multiplicatively.
What is weighted mean used for?
Weighted mean is used when some values contribute more than others. For example, calculating a course grade where exams count more than homework — each score is multiplied by its weight before averaging.
Can the mean be a value not in the data set?
Yes. The mean is often a value that does not appear in the original data. For example, the mean of 1 and 2 is 1.5, which is not in the set.