μ Mean Calculator (Arithmetic, Geometric, Harmonic)

Mean Results

Types of Mean

The "mean" is a measure of central tendency. There are several types of mean, each useful in different contexts.

Arithmetic Mean

AM = (x₁ + x₂ + ... + xₙ) / n

Geometric Mean

GM = ⁿ√(x₁ × x₂ × ... × xₙ)

Harmonic Mean

HM = n / (1/x₁ + 1/x₂ + ... + 1/xₙ)

For any dataset: HM ≤ GM ≤ AM (AM-GM-HM inequality)

Frequently Asked Questions

What is arithmetic mean? ▼
Arithmetic mean is the most common type of mean — it's the sum of all values divided by the count. For 2, 4, 6, 8: AM = 20/4 = 5.
When should I use geometric mean? ▼
Geometric mean is best for data that grows multiplicatively, such as investment returns, population growth, or any ratio-based data.
What is harmonic mean used for? ▼
Harmonic mean is used for rates and speeds. For example, if you travel 60 km/h for the first half and 40 km/h for the second half, the average speed uses harmonic mean.