The standard deviation is a measure of the amount of variation or dispersion of a set of values. It tells you, on average, how far each value lies from the mean of the set. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range. The standard deviation is calculated as the square root of the variance. It is expressed in the same unit as the data.
The standard deviation is widely used in statistics, finance, and industrial settings to test models against real-world data. In finance, it is often used as a measure of the risk associated with price fluctuations of a given asset or the risk of a portfolio of assets. In normal distributions, a high standard deviation means that values are generally far from the mean, while a low standard deviation indicates that values are clustered close to the mean.
To calculate the standard deviation, you can follow these steps:
- Calculate the mean of the data set.
- For each data point, subtract the mean and square the result.
- Sum the squared differences.
- Divide the sum by the number of data points minus one.
- Take the square root of the result.
The standard deviation is a useful measure of spread for normal distributions, where data is symmetrically distributed with no skew. It is a summary measure of the differences of each observation from the mean.
