CBSE Class 11 Economics Measures Of Dispersion Notes

MEASURES OF DISPERSION 

1. Dispersion refers to the variation of the items around an average. According to Dr Bowley : “Dispersion is the measure of variations of items.” To quote CONNOR : - “Dispersion is a measure of the extent to which the individual items vary.”

2. Objectives of Dispersion :

(i) To determine the reliability of an average

(ii) To compare the variability of two or more series

(iii) It serves the basis of other statistical measures such as correlation etc.

(iv) It serves the basis of statistical quality control.

3. Properties of a good measure of dispersion:

(i) It should be easy to understand.

(ii) It should be simple to calculate

(iii) It should be uniquely defined.

(iv) It should be based on all observations.

(v) It should not be unduly affected by extreme items.

4. Measures of dispersion may be either absolute or relative.
Absolute measures of dispersion are expressed in the some units in which data of the series are expressed i.e., rupees kgs, tons etc. where as relative measures of dispersion are independent of the units of measurement. They are expressed in percentage these are used to compare two or more series which are expressed in different units.

5. Absolute measures of dispersion are:-

(i) Range

(ii) Quartile Deviation

(iii) Mean Deviation

(iv) Standard deviation and variance.

 6. Relative measures of dispersion are:-

(i) Coefficient of Range.

(ii) Coefficient of Quartile Deviation

(iii) Coefficient of mean Deviation

(iv) Coefficient of standard Deviation

(v) Coefficient of variation

7. Besides the above measures of dispersion there is a graphic method of studying dispersion, known as Lorenz curve.

8. Range is the simplest measure of dispersion : -

It is the difference between the largest and smallest value of the distribution. Computation of range:- It is calculated as Range = L - S
Coefficient of Range = L-S/ L-S

9. Merits of Range :-

(i) It is simple to understand and easy to calculate

(ii) It is widely used in statistical quality control.

10. Demerits of Range=

(i) It is affected by extreme values in the series.

(ii) It can not be calculated in case of open-ended series.

(iii) It is not based on all the items of the series.

11.Inter quartile range and quartile deviation are another measures of dispersion. Inter-quartile range is the difference between the upper quartile Q₃ and lower quartile Q₁. Quartile deviation is half of the difference between the upper quartile and lower quartile i.e. half of the inter-quartile range.

Computation of Inter-quartile Range and Quartile Deviation:-

Inter- quartile Range:- Q₃ – Q₁

Quartile Deviation (Q.D) : = Q₃ - Q₁ / 2

Co. efficient of Q.D : = Q₃ - Q₁ / Q₃ + Q₁ 

12. Merits of Quartile Deviation:-
(i) It is easy to compute.
(ii) It is less affected by extreme items
(iii) It can be computed in open-ended series.

13. Demerits of Quartile Deviation :-
(i) It ignores half i.e. 50% of the items.
(ii) It is useful only for rough study.
(iii) It is not based on all observations.

14. Mean deviation :- It is defined as the arithmetic average of the absolute deviations (ignoring signs) of the various items from a measure of central tendency ; i.e. mean or median. Generally, mean deviation is calculated from median because the sum of the absolute deviations taken from median is minimum or least.

16. Merits of mean Deviation:-
(i) It is based on all observations.
(ii) It is least affected by extreme items.
(iii) It is simple to understand and easy to calculate.

17. Demerits of mean Deviation:-
(i) It ignores ± signs in deviations
(ii) It can not be computed with open - ended series.
(iii) It is not well defined measure because it is calculated from different
averages (Mean, Median & Mode)
(iv) It is difficult to compute when X or M comes in fractions.

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