DISPERSION Introduction, Objectives/Importance, Absolute & Relative Measures, Methods
🚩Timestamps:-
00:23 Session Agenda
02:38 What is Dispersion
10:24 Definition
11:13 how is dispersion different from Average of the series
13:09 Basic Objective Related to the Measurement of Dispersion
14:05 Objectives Related to the Measurement of Dispersion
18:02 ABSOLUTE AND RELATIVE MEASURES OF DISPERSION
21:55 Methods of Measuring Dispersion (names only)
22:55 Why should we measure Dispersion about some particular value
29:42 Concluding Remarks
Learning Outcomes:-
Through this module, you will gain understanding on:-
1. What is Dispersion? Definition
2. how is dispersion different from Average of the series -
3. Objectives Related to the Measurement of Dispersion -
4. ABSOLUTE AND RELATIVE MEASURES OF DISPERSION -
5. Methods of Measuring Dispersion (names only)
6. Why should we measure Dispersion about some particular value?
What is Dispersion?
Average indicates representative value of the series around which other values of the series tend to converge. So that average represents the series as a whole.
One may now be keen to know how far the various values of the series tend to disperse from each other, or from their average. This brings us to yet another important branch of statistical methods, viz., Measures of Dispersion. Only when we study dispersion along with average of a series that we can have a comprehensive information about the nature and composition of a statistical series.
Wages paid to 5 workers in three factories: A, B, C –
|
Factory A |
Factory B |
Factory C |
|
400 400 400 400 400 no variation between the average wage and the wages paid |
350 380 400 420 450 small variation |
50 75 400 725 750 large variation min wage = Rs 50 max wage = Rs 750 It shows that mean and median do not provide complete information about the composition and character of a series. |
In all the three factories, the arithmetic mean and median is same, i.e., 400.
In order to get a comprehensive picture of the series, we should study measures of dispersion as well.
Definition
Dispersion is the measure of the variation of the items.
Dispersion measures the degree to which numerical data tend to spread about an average value.
how is dispersion different from Average of the series -
|
dispersion |
Average |
|
· different items tend to differ from each other and from their average · Dispersion measures the extent of this difference |
· refers to central tendency of the series · represents behaviour of all items in the series · value of the series around which other values of the series tend to converge |
What is the Basic
Objective Related to the Measurement of Dispersion?
It is to know about the composition of the statistical series by estimating the extent to which different items of the series tend to move away from their average value or the central tendency.
Objectives Related
to the Measurement of Dispersion -
(1) To know the variation of different values of the items from the average value of a series.
(2) To know about the composition of a series or the dispersal of values on either sides of the central tendency.
(3) To know the range of values (i.e., difference between the highest and the lowest value).
(4) To compare the disparity between two or more series in order to find out the degree of variation.
lack of similarity or equality; inequality; difference
(5) To know whether the central tendency truly represents the series or not
ABSOLUTE AND RELATIVE MEASURES OF DISPERSION -
(i) Absolute
Measure
· dispersion of the series is expressed in terms of the original unit of the series
· Thus, dispersion of price series would be expressed in terms of rupees; dispersion of weight series would be expressed in terms of kilograms; and so on.
· For example, if one states that the average wage of a group of the workers is Rs 100 and dispersion of the wage is Rs 10, one is referring to absolute dispersion.
· Absolute measure of dispersion is used when only one set of statistical distribution is under consideration. It cannot be used when comparison is involved across two or more sets of statistical series with different units of measurement (like 'rupee' in one case and 'kilogram' in the other).
(ii) Relative
Measure
· expresses the variability of data in terms of some relative value or percentage.
· Thus, if one states that 26 per cent of the people in India are below poverty line, one is referring to the relative variability of data.
· In such cases, absolute variability is divided by the mean value of the series or percentage of the absolute variability determined.
· This measure of dispersion is used when one studies two or more series simultaneously.
· Relative measure of dispersion is known Coefficient of Dispersion
Methods of Measuring Dispersion
|
Absolute Measure |
relative measures |
|
Range |
Coefficient of Range |
|
Quartile Deviation; Inter Quartile Range |
Coefficient of Quartile Deviation |
|
Mean Deviations |
Coefficient of Mean Deviation |
|
Standard Deviation |
Coefficient of Standard Deviation, Coefficient of Variation
|
|
Lorenz Curve |
|
Why should we
measure Dispersion about some particular value?
· All measures of dispersion do not measure variation about some particular value of the series.
· Range, for example, is simply the difference between the highest and the lowest values of a statistical series.
· Likewise, quartile deviation is defined as half of the difference between Q3 (third quartile) and Q1 (first quartile).
· But measures of dispersion like mean deviation and standard deviation are worked out as deviations from some central tendency of the statistical series.
· Deviations from some central tendency (or central value like mean or median) of the series offers a better picture of dispersion. Why?
Because:
(i) then we can assess how precise is the central tendency as the representative value of all the observations in the series. Greater value of dispersion implies lesser representativeness of the central tendency and vice versa, and
(ii) we can precisely assess how scattered are the actual observations from their representative value. Actual observations may show both a positive variation as well as negative variation from the observed central tendency of the series.
A summary measure of variation (which is what a measure of dispersion focuses on) is possible only when all the variations are duly considered.
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What is Dispersion, Definition, how is dispersion different from Average of the series, Basic Objective Related to the Measurement of Dispersion, Objectives Related to the Measurement of Dispersion, ABSOLUTE AND RELATIVE MEASURES OF DISPERSION, Methods of Measuring Dispersion (names only), Why should we measure Dispersion about some particular value | Measures of Dispersion | 11th Commerce | by @statomics11comm
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