### Theory:

Measures of Dispersion of a data provide an idea of how observations spread out (or) scattered throughout the data.
Measures of Dispersion is also known as Measures of Variation.
Different Measures of Dispersion:
The different measures of dispersion are:

1. Range
2. Mean Deviation
3. Quartile Deviation
4. Standard Deviation
5. Variance
6. Coefficient of Variation

Let us discuss what is a range for a given set of data.

Range:
The difference between the largest value and the smallest value in the given set of data is called Range.
Range $$R$$ $$=$$ Largest value $$L$$ $$-$$ Smallest value $$S$$

Coefficient of range $$=$$ $$\frac{L - S}{L + S}$$
Example:
Find the range of the given data: $$23, 64, 56, 42, 11$$.

Solution:

Largest value $$L$$ $$=$$ $$64$$

Smallest value $$S$$ $$=$$ $$11$$

Range $$R$$ $$=$$ $$L - S$$

$$=$$ $$64 - 11$$

$$=$$ $$53$$

Therefore, the of the given set of data is $$53$$.
Important!
If the given data represented using class interval has the frequency of initial class as zero, then the next class will be considered for the calculation of range.