Math, asked by muskanahlawat2001, 11 hours ago

10) a) A panel of judge A and B graded seven candidates and awarded the following marks:

[6]

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 judgments?​

Answers

Answered by amitnrw
10

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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