Probability and Statistics

Variance and Standard Deviation

Info

Mean can be represented as $\bar{x}$ or $\mu$ where $\bar{x}$ is the mean of the sampled population and $\mu$ is the mean of the entire population.

Variance $({\sigma }^2)$ - Measure of the spreading of the data from its mean. Standard Deviation $(\sigma )$ - Square root of the variance.

Steps to Find

1. Calculate the distance from the mean for each variable/data point and square the result to account for negative values.

$$(x_n-\mu {)}^2$$

2. Calculate the mean to determine variance.

$${\sigma }^2=\frac{1}{N}\sum _{n=1}^N(x_n-\mu {)}^2$$

3. Square the result for standard deviation.

$$\sigma =\sqrt{\frac{1}{N}\sum _{n=1}^N(x_n-\mu {)}^2}$$