In statistics, standard deviation is defined as:

Standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a set of values. Specifically, it calculates how much individual data points deviate from the mean (the average) of the dataset. A low standard deviation indicates that the data points tend to be close to the mean, whereas a high standard deviation indicates that the data points are spread out over a wider range of values.

When assessing a dataset, the mean provides a central value, but it doesn't give any indication of the variability of the data. This is where standard deviation becomes essential; it complements the mean by providing insight into the distribution of values around that mean. Standard deviation is calculated using the average of the squared deviations from the mean, followed by taking the square root of that average.

Understanding standard deviation is crucial in fields like biomedical engineering, where it helps in evaluating data from experiments and tests, determining the reliability of measurements, and understanding the expected variation in biological responses. By focusing on how scores vary around the mean, standard deviation provides clear insights into the data's spread and the degree of consistency across observations.