Standard deviation in statistics, typically denoted by σ, is a measure of variation or dispersion between values in a set of data. It indicates how spread out the data points are. A lower standard deviation means data points are closer to the mean, while a higher standard deviation means a wider range of values.
The population standard deviation, σ, is used when the entire population can be measured. It's calculated using the square root of the variance of a given data set.
Example:
μ = (1+3+4+7+8) / 5 = 4.6
σ = √[(1 - 4.6)² + (3 - 4.6)² + ... + (8 - 4.6)²] / 5 = 2.577
The sample standard deviation, s, is used when you can't measure the entire population and must use a sample. It's a corrected version of the equation, considering the sample size.
Standard deviation is widely used in various fields, including quality control, climate analysis, and finance. It helps measure variability and assess risk.