Dispersion is a statistical term that describes the size of the range of values expected for a particular variable.
It is mainly useful to find the relationship between the set of data. The tendency of a data scattered over a range is called as Dispersion. It is one of the most important frequency distribution. In other simple words, it can be called as a spread or variation.

Dispersion is defined as the measurement including the average deviation, variance and the standard deviation. The most widely used measure of dispersion are standard deviation and variance.

The mean value of a data gives the information about the set. Many sets have the same values. And to find out how sets are different, we need more information. And that can be done by looking at, how the data is spread out, or dispersed.

There are many ways to measure these dispersion and few of them are:
  1. Mean Absolute Deviation
  2. Range
  3. Standard Deviation
  4. Variance
  5. Inter-quartile range

Mean Absolute Deviation: The difference between the individual values in the data set and the mean got from the average absolute values is called as Mean Absolute Deviation.
This method measure the average distance between the values in the data and the mean.

$Mean\ Absolute\ Deviation = $$\frac{\sum(x_i - \overline{x})}{n}$

Here $\bar{x}$, is the arithmetic mean of data set.

Range: This is one of the most simplest method of measuring dispersion. Range can be found by subtracting lowest value from highest value and for this reason the range is often unreliable for the measure of dispersion as it depended on only two values in the set.

For example:
Range of following data: 22, 35, 37, 42, 30, 46, 48, 53, 54, 64
Highest value = 64
Lowest value = 22
=> Range = 64 - 22 = 42
The Range is 42. This gives us a very less knowledge on how the values are dispersed.

Standard Deviation: In simple words, standard deviation is the square root of the variance.
Formula of Standard Deviation
Variance: The variance is the measure of how far a set of number is spread out. It is the average squared difference of the data from the mean score of a distribution.
Formula of Variance
Inter-Quartile Range: Inter-quartile range is the difference between the first and the third quartile range. It measures the spread of the middle 50% of an ordered data set.
Formula Inter Quartile RangeHere,
Q3 is the third quartile
Q1 is the first quartile