\[\begin{aligned}
\mu_w &= \frac{\sum (w x)}{\sum w} \\
\sigma_w^2 &= \frac{\sum \left(w(x-\mu_w)^2\right)}{\sum w}
\end{aligned}\]
Variables
muarithmetic mean
varvariance
sigmastandard deviation
sumXsum of all values
sumSqsum of squared deviations
sumDev2total squared deviation
nnumber 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