Standard deviation calculator
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:
- Calculate the mean of the dataset.
- For each value in the dataset, subtract the mean and square the result.
- Sum the squared differences from step 2.
- Divide the sum by the number of values in the dataset minus 1.
- 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))
- 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.