Dispersion
The degree to which numerical data tend to spread about an average value is called the variation or dispersion of data. Dispersion can also be called the amount of deviation or scattering of observations from the average.Measures of dispersion may be classified into:
- Absolute measures of dispersionâ€‹
- Range
- Mean deviation
- Standard deviation
- Quartile deviation
- Relative measures of deviation
- Coefficient of range
- Coefficient of mean deviation
- Coefficient of variation
- Coefficient of quartile deviation
Difference Between Absolute and Relative Measures of Dispersion
Absolute Measures of Dispersion |
Relative Measures of Dispersion |
Dependent on the unit of the variable |
Independent of the unit of the variable |
Not considered for comparing two or more distributions |
Considered for comparing two or more distributions |
Easy to compute and understand |
Compared to absolute measures of dispersion, relative measures are difficult to compute and understand |
Range
For a given set of observations, the difference between the highest and the lowest observation is called range.
If H and L denote the highest and lowest observations, then
Range = H â€“ L
Corresponding relative measure of dispersion is
For a grouped frequency distribution, range is the difference between the highest and lowest class boundaries.
â‚¹80, â‚¹65, â‚¹90, â‚¹60, â‚¹75, â‚¹70, â‚¹72, â‚¹85
Range = 90 â€“ 60 = â‚¹30 (Since Range = H â€“ L.)
Properties of Range
Range remains unaffected due to a change of origin, but is affected in the same ratio due to a change in scale.
Thus, if two variables x and y are related as y = a + bx, where, a and b are any constants, then range of y is given by Ry= | b | Ã— Rx (where Rx is the range of x).
Merits
- It can be easily understood.
- It is easy to calculate and it is the simplest method of measuring dispersion.
- It lends itself to algebraic treatment.
- It is an absolute measure of dispersion.
Demerits
- It is too indefinite to be used as a practical measure of dispersion, because it depends entirely upon the extreme values.
- It is not based on all the observations.
- It is affected by sampling fluctuations.