Standard Deviation

What is standard deviation?

Standard deviation measures how much individual values differ from the mean. A small standard deviation indicates that values are clustered closely, while a large one indicates greater spread.

Standard deviation formula

Standard deviation is the square root of variance. There are two common formulas depending on whether you are working with a population or a sample.

Example

Why is standard deviation important?

Standard deviation is widely used to measure risk, variability, and consistency in data. It plays a central role in statistics, finance, quality control, and data science.

Standard deviation vs variance

Variance uses squared units, which can be difficult to interpret. Standard deviation converts variance back into the original units, making it easier to understand in real-world applications.

When should you use standard deviation?

Standard deviation is most useful when data is approximately normally distributed and when understanding variability is more important than extreme values.