Standard deviation
Standard Deviation
Standard deviation (pronounced: /ˈstandərd dɪviˈeɪʃən/) is a statistical term that measures the amount of variability or dispersion around an average.
Etymology
The term "standard deviation" was first used in 1893 by the English statistician Karl Pearson. It is derived from the concept of deviating from the "standard" or average.
Definition
Standard deviation is defined as the square root of the variance. It is denoted by the Greek letter sigma (σ) when referring to a population and by the Latin letter 's' when referring to a sample.
Calculation
The calculation of the standard deviation involves several steps. First, the mean (average) of the data set is calculated. Then, the difference between each data point and the mean is found. These differences are then squared, and the average of these squared differences is calculated. This value is the variance. The square root of the variance gives the standard deviation.
Related Terms
- Mean: The average value in a data set.
- Variance: The average of the squared differences from the mean.
- Population: The entire group that you want to draw conclusions about.
- Sample: A subset of the population.
- Data set: A collection of related sets of information that is composed of separate elements but can be manipulated as a unit by a computer.
- Dispersion: The state of being spread out or dispersed.
Uses
Standard deviation is widely used in fields such as finance, physics, engineering, and medical research. It helps researchers and analysts understand the variability within a data set or population, and it is a key parameter in many statistical tests and models.
External links
- Medical encyclopedia article on Standard deviation
- Wikipedia's article - Standard deviation
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