BrainyCalculators
Login
Advertisement

x̄ Mean Calculator

Calculate the arithmetic mean, geometric mean, and harmonic mean for any data set. Enter numbers separated by commas or spaces to get all three averages instantly, plus sum, min, max, and range.

Mean Formulas

Arithmetic Mean
x̄ = (x₁ + x₂ + … + xₙ) / n
Geometric Mean
GM = (x₁ × x₂ × … × xₙ)^(1/n)
Harmonic Mean
HM = n / (1/x₁ + 1/x₂ + … + 1/xₙ)

How to Calculate the Mean

  1. 1
    Enter Your Numbers
    Type or paste your numbers separated by commas or spaces into the input field. Decimals and negatives are supported.
  2. 2
    Click Calculate
    Press Calculate or just start typing — results update automatically as you enter data.
  3. 3
    Read All Three Means
    The calculator shows arithmetic, geometric, and harmonic mean alongside count, sum, min, max, and range.
  4. 4
    Review Sorted Data
    The sorted data list helps you visually inspect the distribution and spot outliers.

Worked Example

Data set: 2, 4, 8

Count = 3
Sum = 2 + 4 + 8 = 14
Arithmetic Mean = 14 ÷ 3 = 4.667
Geometric Mean = (2 × 4 × 8)^(1/3) = 64^(1/3) = 4
Harmonic Mean = 3 / (1/2 + 1/4 + 1/8) = 3 / 0.875 = 3.429

Frequently Asked Questions

The arithmetic mean (average) is the sum of all values divided by the count. It is the most common measure of central tendency and works well for data without extreme outliers or skew.

Use geometric mean when dealing with quantities that multiply together, such as growth rates, investment returns, or ratios. It is always less than or equal to the arithmetic mean and is undefined for negative numbers.

Harmonic mean is best for averaging rates and speeds (e.g. miles per hour over different legs of a trip). It is the most appropriate average when the data represents unit rates. It is undefined if any value is zero.

Mean is the sum divided by count; median is the middle value when sorted. Mean is sensitive to outliers while median is not. For skewed data (e.g. income), median is often a better measure of typical value.

Related Calculators

M̃ Statistics

Median Calculator

Find the median (middle value) of any data set, sorted and unsorted.

Calculate now
Mo Statistics

Mode Calculator

Find the mode (most frequent value) of any data set, including multimodal sets.

Calculate now
📉 Statistics

Standard Deviation Calculator

Calculate mean, variance, and standard deviation for any data set.

Calculate now