Statistics

Mean, Variance and Standard Deviation Link to heading

Mean is the average of a set of numbers. It is calculated by adding all the numbers in the set and dividing by the number of elements in the set. It is denoted by the symbol $\mu$.

$$ \mu = \frac{1}{m} \sum_{i=1}^{m} x_i $$

where:

• $\mu$ is the mean
• $m$ is the number of elements in the set
• $x_i$ are the individual elements in the set

Variance is a measure of how spread out the numbers in a data set are. It is calculated by taking the average of the squared differences between each number and the mean. It is denoted by the symbol $\sigma^2$.

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

where:

• $\sigma^2$ is the variance
• $m$ is the number of elements in the set
• $x_i$ are the individual elements in the set

Standard Deviation is the square root of the variance. It is denoted by the symbol $\sigma$.

$$ \sigma = \sqrt{\sigma^2} $$

The standard variation is the measure of how spread out the numbers in a data set are in the unit of the data set. Whereas the variance is the measure of how spread out the numbers in square units of the data set.