Question

panel of judge A and B graded seven candidates and awarded the following
Candidate 1 2 3 4 5 6 7
Marks by A 48 35 38 49 50 25 35
Marks by B 38 34 39 56 48 32 45
An eighth candidate was awarded 36 marks by judge A while judge B was not present. If judge B was also
present, how many marks would you expect him to be awarded to the eighth candidate assuming that the
same degree of relationship exists in their judgment

Answer 1

Given : A panel of judge A and B graded seven candidates and awarded the following marks:

Candidate 1 2 3 4 5 6 7

Marks by A 48 35 38 49 50 25 35

Marks by B 38 34 39 56 48 32 45

eighth candidate was awarded 36 marks by judge A

To Find : Marks expected by Judge B for 8th candidate

Solution:

Marks by A = x

Marks by B = y

y = a + bx

$y-\overline{y}=b(x-\overline{x})$

$b=\dfrac{\sum(x-\overline{x}).(y-\overline{y})}{\sum(x-\overline{x})^2}$

$\overline{x}=\dfrac{48+35+38+49+50+25+35}{7} =40$

$\overline{y}= \dfrac{292}{7}$

$x \quad y \quad x-\overline{x} \quad y-\overline{y} \quad (x-\overline{x}) (y-\overline{y}) \quad(x-\overline{x})^2$

48 38 8 -3.71 -29.71 64

35 34 -5 -7.71  38.57 25

38 39 -2 -2.71 5.43 4

49 56 9 14.29 128.57 81

50 48 10 6.29 62.86 100

25 32 -15 -9.71 145.71 10

35 45 -5 3.29 -16.43 10

       335.00 294

b =  335/294  

y  -  292/7   = 335/294 (x  - 40)

=> 294y  -  12264 = 335x  -  13400

=> 294y  = 335x-  1136

=> y  =  1.14x  - 3.864

x = 36

=> y =  37.2  

37.2    marks are expected

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