Question

The following data based 450 students are given for marks in statistics and economic at certain examination.estimate the average marks in economics of the candidate who obtained 50
Mean marks statistics (40) 12economics (48) 16
Sum of products of deviation of marks from their respective mean =42075

Answer 1

Given : 450 students are given for marks in Statistics and Economics at a certain examination.

Statistics Mean marks = 40

Economics Mean marks = 48

Statistic Standard Deviation = 12

Economics standard deviation = 16

Sum of products of deviations of marks from their respective mean = 42075.​

To Find :  Estimate the average marks in Economics of the candidates who obtained 50 marks in Statistics

Solution:

Statistics marks = x

Economics marks = y

Regression equation of x on y

$x-\overline{x}=r\dfrac{\sigma_x}{\sigma_y}( y-\overline{y})$

$r=\dfrac{\sum d_x.d_y}{n\sigma_x.\sigma_y}$

$\sum d_x.d_y = 42075, n=450, \sigma_x=12,\sigma_y=16$

=> r  = 42075/(450 * 12 * 16)

=> r ≈ 0.487

$x-\overline{x}=r\dfrac{\sigma_x}{\sigma_y}( y-\overline{y})$

$\overline{x}= 40, \overline{y}=48$

x - 40  = 0.487 (12 / 16) (y - 48)

=> x - 40  = 0.365(y - 48)

=> x  = 0.365y + 22.469

As value of x is given and we need to find y

so

Regression equation of y on x

$y-\overline{y}=r\dfrac{\sigma_y}{\sigma_x}( x-\overline{x})$

y - 48  =  0.487 ( 16/12) (x - 40)

=> y - 48  = 0.6493 (x - 40)

=> y - 48 = 0.6493x  - 25.97

=> y = 0.6493x  + 22.03

x = 50

=> y =  54.495

=> y  ≈ 54.5

the average marks in Economics of the candidates who obtained 50 marks in Statistics :   54.5

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