Mean

Tags

PAS

Cegep/2

Word count

108 words

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1 minute

Sum of measurements divided by the number of measurements
Measure of central tendency
Syn. expected value (of a random variable)

Sample mean:

$$\bar{x}=\frac{\sum _{i=1}^n{x}_i}{n}$$

Population mean:

$$\mu =\frac{\sum _{i=1}^N{x}_i}{N}$$

For discrete classes:

$$\bar{x}=\frac{\sum _{i=1}^c{n}_i{x}_i}{n}$$

For continuous classes:

$$\bar{x}=\frac{\sum _{i=1}^c{n}_i{c}_i}{n}$$

Properties

$$\begin{array}{rl}E(\bar{X})& =\mu \\ Var(\bar{X})& =\frac{{\sigma }^2}{n}\\ Z& =\frac{\bar{x}-\mu }{\frac{\sigma }{\sqrt{n}}}\end{array}$$

For linear transformation:

$$E(Y)=E(aX+b)=aE(X)+b$$

For independent variables:

$$E(T)=E(X\pm Y)=E(X)\pm E(Y)$$

Contributors

Ajitani Hifumi

Changelog

Last edited about 2 hours ago

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7a6541d-feat: feet