Search for a tool
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.

Results

Mean of Numbers -

Tag(s) : Statistics, Data Processing

Share
dCode and more

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!

Feedback and suggestions are welcome so that dCode offers the best 'Mean of Numbers' tool for free! Thank you!

# Mean of Numbers

## Mean Calculator

 Compute Arithmetic Mean (Classic) Harmonic Mean Quadratic Mean

### 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 $\sqrt[3]{ 1 \times 1.5 \times 2 } \approx 1.4422$

### 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 $\sqrt{\frac{4^2+5^2+6^2}{3}} = \approx 5.06$

### How to find back numbers from the mean value?

It is impossible to find the original numbers from the mean value. There are endless lists of possible numbers with the same mean value.

Example: 10,20,30 has the same arithmetic mean as -100,0,1,99,100

## Source code

dCode retains ownership of the "Mean of Numbers" source code. Except explicit open source licence (indicated Creative Commons / free), the "Mean of Numbers" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Mean of Numbers" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Mean of Numbers" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!
Reminder : dCode is free to use.

## Cite dCode

The copy-paste of the page "Mean of Numbers" or any of its results, is allowed (even for commercial purposes) as long as you credit dCode!
Exporting results as a .csv or .txt file is free by clicking on the export icon
Cite as source (bibliography):
Mean of Numbers on dCode.fr [online website], retrieved on 2024-09-14, https://www.dcode.fr/mean

## Need Help ?

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!

Feedback and suggestions are welcome so that dCode offers the best 'Mean of Numbers' tool for free! Thank you!

https://www.dcode.fr/mean
© 2024 dCode — El 'kit de herramientas' definitivo para resolver todos los juegos/acertijos/geocaching/CTF.

Feedback