Question

If y+2x = 10 , mean =3 and var (y) = 25 , then C.V. of y is. (a) 100% , (b) 150 % , (c) 125% , (d) 50%.

Answer 1

Please see the attachment

Answer 2

The C.V. of y is (c) 125 %.

Given: y + 2x = 10 , mean = 3 and var (y) = 25.

To Find: The C.V of y.

Solution:

• The C.V can be calculated by the formula;

       C.V of y = ( S.D of y / Mean of y ) × 100                                 ...(1)

Where S.D = Standard deviation, C.V = Covariance.

• The standard deviation can be calculated by the formula,

        S.D = √( Variance )

Coming to the numerical, we are given;

        y + 2x = 10                                                                                ...(2)

The mean of x ( x' ) = 3

The variance of y ( Var(y) ) = 25

So, the S.D of y = √Var(y) = √25

                           = 5

Putting x' = 3 in (2), we can find the mean of y ( y' );

           y' + 2x' = 10

      ⇒  y' + 2×3 = 10

      ⇒  y'  =  4                                                                        ....(3)

Putting (3) in (1), we get;

           C.V of y = ( S.D of y / Mean of y ) × 100  

       ⇒ C.V of y = ( 5 / 4 ) × 100

       ⇒ C.V of y = 125 %

Hence, the C.V. of y is (c) 125 %.

#SPJ2