Standard deviation is a measure of how much the values in a dataset vary from the average (mean) value. It is a commonly used statistic in many fields, including science, engineering, finance, and social sciences.

To calculate the standard deviation of a dataset:

1. Calculate the mean of the dataset.
2. For each value in the dataset, subtract the mean and square the result.
3. Sum the squared differences from step 2.
4. Divide the sum by the number of values in the dataset minus 1.
5. Take the square root of the result from step 4.

The formula for standard deviation can be written as:

σ = √(Σ(xi – x̄)² / (n – 1))

where:

• σ is the standard deviation
• xi is the ith value in the dataset
• x̄ is the mean of the dataset
• n is the number of values in the dataset

A larger standard deviation indicates that the values in the dataset are more spread out from the mean, while a smaller standard deviation indicates that the values are closer together. Standard deviation is used as a measure of variability or dispersion, and can help to identify outliers or unusual values in a dataset.