Tool to calculate the standard deviation of a list of values. Standard deviation is a statistical value characterizing the dispersion of a sample or distribution.

Standard Deviation - dCode

Tag(s) : Statistics

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*!

The standard deviation measures the dispersion of a value series around its mean. This value, denoted $ \sigma $ (Greek letter sigma lowercase) characterizes how the data $ X $ (random variable) are scattered, their volatility, by measuring the square root of the differences between each value (of the variable) and the mean $ m $ (or expectation). $$ \sigma(X) = \sqrt{ \mathbb{E} \left[(X - m)^{2}\right] } $$

From a list of numbers $ x_i $ of a random variable $ X $ whose distribution is unknown but with a mean $ m $, the formula is $$ \sigma(X)= \sqrt{ \frac{1}{n} \sum_{i=1}^{n}(x_{i}-m)^2 } $$ however, this estimator has a biais and the following formula is preferred $$ \sigma(X)= \sqrt{ \frac{1}{n-1} \sum_{i=1}^{n}(x_{i}-m)^2 } $$

__Example:__ The (unbiased) standard deviation of the series of `3` numbers `4,5,9` whose average is `6` is $ \sqrt{ \frac{1}{3-1} \left( (4-6)^2 + (5-6)^2 + (9-6)^2 \right) } = \sqrt{ 14/2 = 7 } \approx 2.646 $

The value of the standard deviation is the square root of the variance. Knowing the value of the variance $ V $, $ \sigma $ can be calculated with the relation: $$ \sigma(X) = \sqrt{ V(X) } $$

dCode retains ownership of the "Standard Deviation" source code. Except explicit open source licence (indicated Creative Commons / free), the "Standard Deviation" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Standard Deviation" 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 "Standard Deviation" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!

Reminder : dCode is free to use.

The copy-paste of the page "Standard Deviation" 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):

*Standard Deviation* on dCode.fr [online website], retrieved on 2024-09-09,

standard,deviation,volatility,list,value,dispersion,distribution,mean,variance

https://www.dcode.fr/standard-deviation

© 2024 dCode — El 'kit de herramientas' definitivo para resolver todos los juegos/acertijos/geocaching/CTF.

Feedback