Measures of Dis...

The standard deviation of variate $$x$$ is the square root of the A.M. of the squares of all deviations of $$x$$ from the A.M. of observations and we denote it by sigma $$ \displaystyle \left ( \sigma \right ) $$ if  $$ \displaystyle x/f_{i}\left ( i = 1,2,3,...,n \right ) $$ is a frequency distribution, then

$$ \displaystyle \sigma =\sqrt{\frac{1}{N}\sum f_{i}\left ( x_{i}-\bar{x} \right )^{2}} $$           ........(i)

where $$ \displaystyle \bar{x} $$ is the A.M.of the distribution & $$ \displaystyle N=\sum_{i=1}^{n}f_{i} $$

The square of the standard deviation is called the variance & given by

$$ \displaystyle \sigma ^{2}=\frac{1}{N}\sum_{i=1}^{n}f_{i}\left ( x_{i}-\bar{x} \right )^{2} $$     ........(ii)

The calculation of coefficient of dispersion & coefficient of variation are count down by $$ \displaystyle \frac{\sigma }{\bar{x}} $$ & $$ \displaystyle \frac{\sigma }{\bar{x}}\times 100 $$ respectively.

If deviation of $$x$$ are measured from an assumed mean $$A$$ then root mean square deviation of $$x$$ is denoted by $$S$$ and given by

$$ \displaystyle S= \sqrt{\frac{1}{N}\sum_{i=1}^{n}f_{i}\left ( x_{i} -A\right )^{2}} $$ 

which set up the relationship between S.D. and Root mean square deviation given by $$ \displaystyle S^{2}=\sigma ^{2}+d^{2}\left ( Where, d=\sum_{i=1}^{n} x_i-A \right ) $$

Consider the frequency distribution

On the basis of above information answer the following questions.

The standard deviation of variate $$x$$ is the square root of the A.M. of the squares of all deviations of $$x$$ from the A.M. of observations and we denote it by sigma $$ \displaystyle \left ( \sigma \right ) $$ if  $$ \displaystyle x/f_{i}\left ( i = 1,2,3,...,n \right ) $$ is a frequency distribution, then

$$ \displaystyle \sigma =\sqrt{\frac{1}{N}\sum f_{i}\left ( x_{i}-\bar{x} \right )^{2}} $$           ........(i)

where $$ \displaystyle \bar{x} $$ is the A.M.of the distribution & $$ \displaystyle N=\sum_{i=1}^{n}f_{i} $$

The square of the standard deviation is called the variance & given by

$$ \displaystyle \sigma ^{2}=\frac{1}{N}\sum_{i=1}^{n}f_{i}\left ( x_{i}-\bar{x} \right )^{2} $$     ........(ii)

The calculation of coefficient of dispersion & coefficient of variation are count down by $$ \displaystyle \frac{\sigma }{\bar{x}} $$ & $$ \displaystyle \frac{\sigma }{\bar{x}}\times 100 $$ respectively.

If deviation of $$x$$ are measured from an assumed mean $$A$$ then root mean square deviation of $$x$$ is denoted by $$S$$ and given by

$$ \displaystyle S= \sqrt{\frac{1}{N}\sum_{i=1}^{n}f_{i}\left ( x_{i} -A\right )^{2}} $$ 

which set up the relationship between S.D. and Root mean square deviation given by $$ \displaystyle S^{2}=\sigma ^{2}+d^{2}\left ( Where, d=\sum_{i=1}^{n} x_i-A \right ) $$

Consider the frequency distribution

On the basis of above information answer the following questions.