Statistical dispersion refers to measures that indicate the variability, spread, or scattering of a distribution in a set of data values. These measures include range, quartiles, absolute deviation, variance, and standard deviation.
The range is the simplest measure of dispersion and is calculated by subtracting the smallest observation (minimum) in the data set from the largest (maximum).
Quartiles divide a rank-ordered data set into four equal parts. The values that divide each part are known as the first, second, and third quartiles; and they are denoted by Q1, Q2, and Q3, respectively.
Absolute deviation is the absolute difference between each data point and the mean of the dataset.
Variance is a measure of dispersion that looks at the average of the squared differences from the Mean.
Standard deviation, perhaps the most commonly used measure of dispersion, is the square root of the variance. A low standard deviation indicates that the data points tend to be close to the mean, while a high standard deviation indicates that the data points are spread out over a wider range.
Understanding these measures is crucial in the field of statistics as it helps in the interpretation of data by providing an insight into the reliability, variability, and general behavior of the data in the set.