Standard deviation refers to the spread of your data from the mean. Variance is the average degree to which each point differs from the mean i.e. the average of all data points. We can relate Standard deviation and Variance because it is the square root of Variance.

Standard deviation and variance are both measures of the spread or dispersion of a dataset, commonly used in statistics and machine learning.

Variance: It is the average of the squared differences from the mean. Mathematically, it is represented as the average of the squared differences between each data point and the mean of the dataset. Variance gives a measure of how much the data values differ from the mean. However, because it involves squaring the differences, it is not in the same unit as the original data.
Standard Deviation: It is the square root of the variance. Standard deviation provides a measure of the amount of variation or dispersion of a set of values. Unlike variance, standard deviation is in the same unit as the original data, making it more interpretable. It measures the average distance of each data point from the mean.

The relationship between standard deviation and variance is that standard deviation is the square root of the variance. Mathematically, you can express it as:

$Standard Deviation = Variance$

So, to calculate the standard deviation, you take the square root of the variance. Conversely, to calculate the variance, you square the standard deviation.

In summary, while both standard deviation and variance provide measures of dispersion, standard deviation is typically preferred in applications where the original units of the data are important, as it is in the same units as the data. However, variance is useful in mathematical calculations and some statistical analyses.