What is the formula to calculate mean and standard deviation in math statistics

The formula for the mean ($\mu$) of a population is:

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

where $x_i$ are the individual data points and $N$ is the total number of data points.

The formula for the sample mean ($\bar{x}$) is:

$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$

where $x_i$ are the individual data points and $n$ is the total number of data points in the sample.

The formula for the population standard deviation ($\sigma$) is:

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

The formula for the sample standard deviation ($s$) is:

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