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σ

Statistics Formulas

Statistical measures, probability distributions, and data analysis formulas.

Arithmetic Mean

xˉ=1n∑i=1nxi\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i

Calculates the average (central value) of a dataset.

Variance

σ2=1n∑i=1n(xi−μ)2\sigma^2 = \frac{1}{n}\sum_{i=1}^{n}(x_i - \mu)^2

Measures the spread of data from the mean.

Standard Deviation

σ=1n∑i=1n(xi−μ)2\sigma = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(x_i - \mu)^2}

Measures the amount of variation in a dataset.

Permutations

P(n,r)=n!(n−r)!P(n,r) = \frac{n!}{(n-r)!}

Number of ways to arrange r items from n items where order matters.

Normal Distribution

f(x)=1σ2πe−12(x−μσ)2f(x) = \frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}

The probability density function for the normal (Gaussian) distribution, describing how data clusters around a mean.