Statistics
Essential formulas and concepts in statistics
Arithmetic Mean (Average)
\(\displaystyle \bar{x} = \frac{x_1 + x_2 + \cdots + x_n}{n}\)
Variables:
Description/Usage:
Gives the central tendency of a data set as the sum of values divided by count. It’s the balance point of the data distribution.
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Standard Deviation (Population)
\(\displaystyle \sigma = \sqrt{\frac{\sum_{i=1}^{N}(x_i - \mu)^2}{N}}\)
Variables:
Description/Usage:
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Normal Distribution (Gaussian PDF)
\(\displaystyle f(x) = \frac{1}{\sigma \sqrt{2\pi}} \exp\!\Big[-\frac{(x-\mu)^2}{2\sigma^2}\Big]\)
Variables:
Description/Usage:
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z-Score (Standard Score)
\(z = \frac{x - \mu}{\sigma}\)
Variables:
Description/Usage:
Converts a value to standard units indicating how many standard deviations \(x\) is above (\(z>0\)) or below (\(z<0\)) the mean. It’s used to compare different distributions or to look up probabilities from standard normal tables.
Mathematical concept visualization