Question

following are the marks scored by students in Kannada and English in an examination estimate the marks in Kannada when the marks in english is 30 mean marks in Kannada and English is 40 and 50 SD of Mark in Kannada and English is 10 and 16​

Answer 1

SOLUTION

TO DETERMINE

Following are the marks scored by students in Kannada and English in an examination

Estimate the marks in Kannada when the marks in English is 30

Kannada English

Mean Marks

40

50

S.D of Marks

10

16

Co-efficient of correlation = 0.3.

EVALUATION

Let y and x denotes the marks scored by students in Kannada and English in the examination

Now by the given condition

r = 0.3

$\sf{ \sigma_y = 10 \: , \: \sigma_x = 16}$

Now

$\displaystyle\sf{ b_{yx} = r. \frac{\sigma_y }{\sigma_x }}$

$\displaystyle\sf{ \implies \: b_{yx} = 0.3 \times \frac{10 }{16 }}$

$\displaystyle\sf{ \implies \: b_{yx} = 0.1875}$

So the regression of y on x

$\displaystyle\sf{ (y - \bar{y}) = b_{yx}(x - \bar{x})}$

$\displaystyle\sf{ \implies \: (y - 40) = 0.1875(x - 50)}$

Now it is given that

x = 30

Thus we get

$\displaystyle\sf{ (y - 40) = 0.1875(30 - 50)}$

$\displaystyle\sf{ \implies \: (y - 40) = 0.1875 \times ( - 20)}$

$\displaystyle\sf{ \implies \: (y - 40) = - 3.75}$

$\displaystyle\sf{ \implies \: y = 36.25}$

FINAL ANSWER

Hence the marks in Kannada when the marks in english is 30 = 36.25

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