Wisdom of Statistics

statistics_wd.md

In the name of God

1. Mean = $\frac{\sum x_i}{n}$ - Used for symmetric data without extreme outliers, as it utilizes all data points for a more precise, mathematical average
2. Median - Sort numbers in order and select middle.
3. Standart deviation - measures data dispersion around the mean, calculated as the square root of variance.

Population Standard Deviation formula

When you have all data.

$\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^{N}(x_i - \mu)^2}$

Where:

Symbol	Meaning
(N)	population size
(x_i)	each value
($\mu$)	population mean
($\sigma$)	population standard deviation

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Sample Standard Deviation formula

When data is only a sample.

$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n}(x_i - \bar{x})^2}$

Where:

Symbol	Meaning
(n)	sample size
($x_i$)	each sample value
($\bar{x}$)	sample mean
(s)	sample standard deviation