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  • Please,please help me In any discrete series (when all values are same), the relationship between MD about mean and SD is

In any discrete series (when all values are same), the relationship between MD about mean and SD is

  • Option 1)

    MD = SD

  • Option 2)

                MD ³ SD

  • Option 3)

    MD < SD

  • Option 4)

    MD £ SD

 

Answers (1)

best_answer

As we learned

 

DISPERSION -

Dispersion means scatteredness, Dispersion measures the degree of scatteredness of the variable about its central value.

-

 

 Let xi/fi; i  = 1, 2,…………., n be a frequency distribution.

Then SD = \sqrt{\frac{1}{N}\sum_{i=1}^{n}\oint_{i}(x_{i}-\bar{x})^{2}}

and  MD = \frac{1}{N}\sum_{i=1}^{n}\oint_{i}|x_{i}-\bar{x}|^{2}

let |x_{i}-\bar{x}|^{2}=z_{i};i=i,2.....n.

Then, (SD)^{2}-(MD)^{2}

=MD = \frac{1}{N}\sum_{i=1}^{n}\oint_{i}z_{i}^{2}-\left [ \frac{1}{N}\sum_{i=1}^{n}\oint_{i}z_{i}\right ]^{2}=\sigma ^{2}\geq 0

Þ         SD ³ MD

 


Option 1)

MD = SD

Option 2)

            MD ³ SD

Option 3)

MD < SD

Option 4)

MD £ SD

Posted by

Himanshu

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