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Mean of Numbers

Tool to calculate the different means of a number list. The mathematic mean of a list of numbers is one of the statistical representations that can illustrate the distribution of the numbers in the list.

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Mean of Numbers -

Tag(s) : Mathematics, Data processing

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# Mean of Numbers

## Mean Calculator

 Compute Arithmetic Mean (Classic) Harmonic Mean Quadratic Mean

Tool to calculate the different means of a number list. The mathematic mean of a list of numbers is one of the statistical representations that can illustrate the distribution of the numbers in the list.

### How to compute an arithmetic mean?

For a list of $n$ values $X = \{x_1, x_2, \dots, x_n \}$. The arithmetic mean has for definition the sum of all the values divided by the number count of values $n$. $$\bar{x} = {1 \over n} \ sum_{i=1}^n{x_i}$$

Example: The list of 4 numbers 12, 14, 18, 13 its average value is (12+14+18+13)/4=14.25

When values are associaed with coefficients (digits or numbers), then use the weighted arithmetic mean.

### How to compute a geometric mean?

For a list of $n$ values $X = \{x_1, x_2, \dots, x_n \}$. The geometric mean has for definition the $n$-th root of the product of values. $$\bar{x}_{geom} = \sqrt[n]{\prod_{i=1}^n{x_i}}$$

The geometric mean is often used to calculate an average interest rate.

Example: The list of 3 values 1, 1.5, 2 has for geometric mean $\sqrt{ 1 \times 1.5 \times 2 } \approx 1.4422$

### How to compute an harmonic mean?

For a list of n values $X = \{x_1, x_2, \dots, x_n \}$. The harmonic mean has for definition the ratio of n to the sum of the inverse of the values. $$\bar{x}_{harm} = \frac{n}{\sum_{i=1}^n \frac{1}{x_i}}$$

The harmonic mean is often used to compute a speed average.

Example: The list of speed values 50 and 100 has for harmonic mean $2/(1/50+1/100) = 66.67$

### How to compute an quadratic mean (Root Mean Square)?

For a list of n values $X = \{x_1, x_2, \dots, x_n \}$. The root mean square (or quadratic mean) has for definition the root of the sum of each value squared, divided by root of n: $$\bar{x}_{quad} = \sqrt{\frac{1}{n}\sum_{i=1}^n{x_i^2}}$$

The RMS is used in electricity to calculate the effective value.

Example: The list of 3 values 4,5 and 6, this distribution has for quadratic mean $\sqrt{\frac{4^2+5^2+6^2}{3}} = \approx 5.06$

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