Tag: maths

Given,   $\sum (x-\bar{x})^2 = 250, n = 10, \bar{x} =50$
Thus standard deviation $ = \sqrt{\cfrac{\sum (x-\bar{x})^2}{n}}=\sqrt{25}=5$
$\therefore$ Coefficient of variation $=\cfrac{\sigma}{\bar{x}}\times 100 =\cfrac{5}{50}\times 100$ % $= 10$%

Given,  mean $\bar{x} = 4,$ and coefficient of variation $=58$ %
If S.D of the given distribution is $\sigma$ then we know that,
Coefficient of variation $=\cfrac{\sigma}{\bar{x}}\times 100$ %
$\Rightarrow 58 = \cfrac{\sigma}{4}\times 100\Rightarrow \sigma = \cfrac{58\times 4}{100}=2.32$

Coeffecient of variation $ = \frac {SD}{AM} \times 100 = \frac {10}{20} \times 100 = 50 $

Coefficient of variation is the ratio of standard deviation to the mean.

Coefficient of variation is given by $CV = \dfrac{SD}{Mean}\times 100 $
$\Rightarrow \dfrac{5}{14}\times 100 = 35.7\%$

Given : standard deviation$(\sigma)=1.2,$ mean$(\overline {X})=10$.

$\sigma=\sqrt{\dfrac{\sum x^2}{n}-\left(\dfrac{\sum x}{n}\right)^2}$

$\begin{array}{l} 3{ x^{ 2 } }+4{ y^{ 2 } }=1 \ Equation\, of\, \tan  gent\, to\, ellipse\, at\, \left( { { x _{ 1 } },{ y _{ 1 } } } \right)  \ 3x{ x _{ 1 } }+4y{ y _{ 1 } }=1 \ \frac { { 3x } }{ { \sqrt { 7 }  } } +\frac { { 4y } }{ { \sqrt { 7 }  } } =1 \ { x _{ 1 } }=\frac { 1 }{ { \sqrt { 7 }  } } \, \, \, \, \, { y _{ 1 } }=\frac { 1 }{ { \sqrt { 7 }  } }  \ \left( { \frac { 1 }{ { \sqrt { 7 }  } } ,\frac { 1 }{ { \sqrt { 7 }  } }  } \right)  \ Hence, \ option\, \, A\, is\, correct\, answer. \end{array}$