Standard Deviation vs Variance (Easiest explanation)

Standard deviation and variance are both measures of dispersion or spread in a dataset, but they differ in how they represent this dispersion and their units of measurement.

Variance

Variance is the average of the squared differences between each data point and the mean (average) of the dataset. It is a measure of how much the individual data points deviate from the mean, squared to eliminate negative values that could cancel out positive values.

The formula for calculating variance (for a sample) is:

where Xi represents individual data points, X_mean is the mean of the dataset, and n is the number of data points. For a population, the denominator would be n instead of (n — 1).

Standard Deviation

Standard deviation is the square root of the variance. It is also a measure of dispersion, but unlike variance, it is expressed in the same units as the data points. This makes standard deviation more interpretable and easier to visualize in the context of the dataset.

The formula for calculating standard deviation (for a sample) is:

Standard Deviation (s) = √Σ((Xi — X_mean)²) / (n — 1)

The choice between using n-1 or n in the denominator depends on whether you are working with a sample or a population. Bessel’s correction (n-1) is used when working with a sample to provide an unbiased estimate of the population standard deviation or variance, while n is used when working with a population because there is no need for a correction.

Key differences between Standard Deviation and Variance:

1. Units of measurement: Variance is expressed in squared units of the original data, while standard deviation is expressed in the same units as the original data. This makes standard deviation more intuitive and easier to interpret in the context of the dataset.
2. Interpretability: Standard deviation is generally more interpretable and easier to visualize than variance because it represents the average deviation from the mean in the original units of the data. Variance, being the average of squared differences, can be harder to grasp conceptually.
3. Use in calculations: Variance is often used in mathematical calculations, statistical analyses, and modeling because it has desirable mathematical properties, such as additivity for independent variables. Standard deviation, on the other hand, is more commonly used for descriptive purposes and when reporting results.

In summary, both standard deviation and variance are measures of dispersion in a dataset, but they differ in their units of measurement and interpretability. Standard deviation is more intuitive and easier to visualize, while variance is more suitable for certain mathematical calculations and analyses.