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!
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.
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 online 'Standard Deviation' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (PHP, Java, C#, Python, Javascript, Matlab, etc.) no data, script or API access will be for free, same for Standard Deviation download for offline use on PC, tablet, iPhone or Android !
Please, check our community Discord for help requests!