## Dispersion :

Dispersion refers to the spread of data or information within a group or population. In other words, it is the variation or deviation of individual values from the average or mean. There are two main types of dispersion: measure of dispersion and measure of variability.

Measure of dispersion is a statistical measure that quantifies the amount of spread or scattering of data within a group. Examples of measure of dispersion include range, interquartile range, and standard deviation.

Range is the simplest measure of dispersion, which is calculated by subtracting the minimum value from the maximum value in a data set. For instance, the range of the following data set {3, 5, 7, 8, 9, 10, 11} is 11-3 = 8.

Interquartile range is another measure of dispersion that is calculated by subtracting the lower quartile (Q1) from the upper quartile (Q3). It is a more robust measure of dispersion than range because it is not influenced by extreme values or outliers. For example, the interquartile range of the data set {3, 5, 7, 8, 9, 10, 11} is (8-5) = 3.

Standard deviation is a measure of dispersion that quantifies the amount of variability or deviation of individual values from the mean. It is calculated by taking the square root of the sum of the squared differences between each value and the mean, divided by the number of values in the data set. For instance, the standard deviation of the data set {3, 5, 7, 8, 9, 10, 11} is 3.5.

Measure of variability, on the other hand, is a statistical measure that quantifies the amount of change or fluctuation of data within a group. Examples of measure of variability include coefficient of variation, mean absolute deviation, and variance.

Coefficient of variation is a measure of variability that is calculated by dividing the standard deviation by the mean, and expressing it as a percentage. It is a useful measure of dispersion because it allows for comparison of data sets with different units or scales. For example, the coefficient of variation of the data set {3, 5, 7, 8, 9, 10, 11} is 100*(3.5/7.5) = 46.7%.

Mean absolute deviation is a measure of variability that is calculated by taking the average of the absolute differences between each value and the mean. It is a useful measure of dispersion because it is not influenced by extreme values or outliers, like the range and interquartile range. For instance, the mean absolute deviation of the data set {3, 5, 7, 8, 9, 10, 11} is (2+2+0.5+0.5+0.5+1+1)/7 = 1.5.

Variance is a measure of variability that is calculated by taking the average of the squared differences between each value and the mean. It is a commonly used measure of dispersion because it is easy to calculate and is not influenced by extreme values or outliers, like the range and interquartile range. For example, the variance of the data set {3, 5, 7, 8, 9, 10, 11} is (4+4+0.25+0.25+0.25+1+1)/7 = 2.5.

In conclusion, dispersion refers to the spread or variation of data within a group or population. There are two main types of dispersion: measure of dispersion and measure of variability. Measure of dispersion includes range, interquartile range, and standard deviation, while measure of variability includes coefficient of variation, mean absolute deviation, and variance. These measures are useful for analyzing and comparing data sets in order to understand the distribution of values and make informed decisions.