Arithmetic Mean, Variance and Standard Deviation

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Arithmetic Mean, Variance and Standard Deviation

\[\begin{aligned} \mu_w &= \frac{\sum (w x)}{\sum w} \\ \sigma_w^2 &= \frac{\sum \left(w(x-\mu_w)^2\right)}{\sum w} \end{aligned}\]

Variables

mu = arithmetic mean

var = variance

sigma = standard deviation

sumX = sum of all values

sumSq = sum of squared deviations

sumDev2 = total squared deviation

n = number of samples

Description

What is this formula?

This set of formulas calculates the arithmetic mean, variance and standard deviation of a dataset. The arithmetic mean represents the central value of the data, variance measures the spread of values around the mean, and standard deviation indicates the typical deviation from the average.

When to use it

Use these formulas when analyzing statistical datasets, experimental measurements, process variability, financial data or engineering test results.

Example

If a dataset contains values distributed around an average, the variance and standard deviation help determine whether the data is tightly grouped or widely dispersed.

Applications

Statistics

Quality control

Engineering analysis

Scientific research

Financial analysis

Data science

Machine learning

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