Explain Merits And Demerits Of Standard deviation
Answers
Step-by-step explanation:
Merits
It is rigidly defined and free from any ambiguity.
Its calculation is based on all the observations of a series and it cannot be correctly calculated ignoring any item of a series.
It strictly follows the algebraic principles, and it never ignores the + and – signs like the mean deviation.
It is capable of further algebraic treatment as it has a lot of algebraic properties.
It is used as a formidable instrument in making higher statistical analysis viz.: correlation, skewness, regression and sample studies, etc.
It is not much affected by the fluctuations in sampling for which is widely used in testing the hypotheses and for conducting the different tests of significance viz. : test, t2 test etc.
In a normal distribution, X¯ ± 1 covers 68.27% of the values for which it is called a standard measure of dispersion.
It exhibits the scatter of dispersion of the various items of a series form its arithmetic mean and thereby justifies its name as a measure of dispersion.
It enables us to make a comparative study of the two, or moiré series, and to tell upon their consistency, or stability through calculation of the important factors viz. co-efficient of variation, variance etc.
It enables us to determine the reliability of the Mean of the two or more series when they show the identical means.
It can be calculated through a good number of methods yielding the same results.
It maintains an empirical relation with other measures of dispersion as under :
Range = 6, QD =2/3 , and MD = 4/5
It has a good number of algebraic properties for which it is possible to determine the number of many connected factors like combined standard deviation of two or more series.
Demerits
It is not understood by a common man.
Its calculation is difficult as it involves many mathematical models and processes.
It is affected very much by the extreme values of a series in as much as the squares of deviations of big items proportionately bigger than the squares of the smaller items.
It cannot be used for comparing the dispersion of two, or more series given in different units.
Answer:
The standard devidtion, like any other devices has certain merits and demerits. These are outlined here as under:
Merits:-
It is rigidly defined and free from any ambiguity.
Its calculation is based on all the observations of a series and it cannot be correctly calculated ignoring any item of a series.
It strictly follows the algebraic principles, and it never ignores the + and – signs like the mean deviation.
It is capable of further algebraic treatment as it has a lot of algebraic properties.
It is used as a formidable instrument in making higher statistical analysis viz.: correlation, skewness, regression and sample studies, etc.
It is not much affected by the fluctuations in sampling for which is widely used in testing the hypotheses and for conducting the different tests of significance viz. : test, t2 test etc.
In a normal distribution, X¯ ± 1 covers 68.27% of the values for which it is called a standard measure of dispersion.
It exhibits the scatter of dispersion of the various items of a series form its arithmetic mean and thereby justifies its name as a measure of dispersion.
It enables us to make a comparative study of the two, or moiré series, and to tell upon their consistency, or stability through calculation of the important factors viz. co-efficient of variation, variance etc.
It enables us to determine the reliability of the Mean of the two or more series when they show the identical means.
It can be calculated through a good number of methods yielding the same results.
It maintains an empirical relation with other measures of dispersion as under :
Range = 6, QD =2/3 , and MD = 4/5
It has a good number of algebraic properties for which it is possible to determine the number of many connected factors like combined standard deviation of two or more series.
Demerits:-
It is not understood by a common man.
Its calculation is difficult as it involves many mathematical models and processes.
It is affected very much by the extreme values of a series in as much as the squares of deviations of big items proportionately bigger than the squares of the smaller items.
It cannot be used for comparing the dispersion of two, or more series given in different units.
Step-by-step explanation:
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