What is the relationship between standard deviation and variance?

The relationship between standard deviation and variance is fundamentally rooted in how they are calculated. Standard deviation is defined as the square root of the variance.

Variance itself is a measure of how much data points in a dataset spread out from the mean and is calculated by taking the average of the squared differences from the mean. Since variance is based on squared values, it can often yield larger numbers, which can make interpretation challenging when assessing variability in the original units of the data. This is where the standard deviation comes into play. Taking the square root of variance transforms it back to the original units of measurement, making it more understandable and directly comparable to the data itself.

This mathematical relationship shows that while variance represents the overall spread of the dataset through squaring, standard deviation provides a more intuitive sense of that spread by reverting to the original measurement scale. Thus, understanding that standard deviation is the square root of variance is key in statistical analysis and interpretation of data.