Standard deviation:
Karl Pearson (1893) introduced the concept of standard deviation. it is the most important and widely used major in studying dispersion. It is regarded as the square root of the arithmetic mean squares of deviation from the arithmetic mean. In short Standard Deviation maybe define as '' root mean square deviation from the mean ". It is actually denoted by the greek small letter sigma (σ).
Characteristic features:
(1) It is the best major of dispersion, it possesses almost all the requisites of good major dispersions.
(2) It is best on all observations, even if one of the observations is change, the standard deviation also changes.
(3) Standard deviation is least affected by the fluctuation of sampling.
(4) The unique property of standard deviation is that it is amenable to algebraic treatment.
(5) A small standard deviation means a high degree of uniformity of the observation as well as the homogeneity of distribution, on the other hand, a large standard deviation is just opposite.
Merits of Standard deviation:
(1) It is based on all the observation.
(2) It is rigidly define.
(3) It is less affected by fluctuation of sampling as compared to the other measures of dispersion .
Demerits of standard deviation:
(1) It is difficult to compute unlike other measures of dispersion.
(2) It is not simple to understand.
(3) It gives more weightage to extreme values.
Application of standard deviation or usage:
(1) It is summarized the deviation of a large distribution 4m mean.
(2) It also helping finding the standard error which determined the difference between mean of two similar samples is by chance or real.
(3) It also helps in finding the suitable size of the sample for valid conclusion.
Variance: The square of the standard deviation is called variance and is denoted by σ2 .
Merits of Standard deviation:
(1) It is based on all the observation.
(2) It is rigidly define.
(3) It is less affected by fluctuation of sampling as compared to the other measures of dispersion .
Demerits of standard deviation:
(1) It is difficult to compute unlike other measures of dispersion.
(2) It is not simple to understand.
(3) It gives more weightage to extreme values.
Application of standard deviation or usage:
(1) It is summarized the deviation of a large distribution 4m mean.
(2) It also helping finding the standard error which determined the difference between mean of two similar samples is by chance or real.
(3) It also helps in finding the suitable size of the sample for valid conclusion.
Variance: The square of the standard deviation is called variance and is denoted by σ2 .
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