Question

# Mean life of following distribution in the following distribution is 57.6 hours. If sum of frequency is 50 then find the missing frequency x and y0âˆ’20720âˆ’40x40âˆ’601260âˆ’80y80âˆ’1008100âˆ’120 5

A
x=7,y=11
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B
x=11,y=7
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C
x=13,y=5
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D
x=8,y=10
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Solution

## The correct option is B x=8,y=10C.I Frequencyfi Mid−valuexi fixi 0−20 7 10 70 20−40 x 30 30x 40−60 12 50 600 60−80 y 70 70y 80−100 8 90 720 100−120 5 110 550 ∑fi=32+x+y ∑fixi=1940+30x+70y ⇒ ∑fi=32+x+y⇒ 50=32+x+y∴ x+y=18 ------- ( 1 )⇒ ¯¯¯x=∑fixi∑fi⇒ 57.6=1940+30x+70y50⇒ 2880=1940+30x+70y⇒ 30x+70y=940∴ 3x+7y=94 ----- ( 2 )Multiplying equation ( 1 ) by 3 we get,⇒ 3x+3y=54 ------ ( 3 )Subtracting equaton ( 3 ) from equation ( 2 ) we get,4y=40∴ y=10Substituting y=10 in equation ( 1 ),x+10=18∴ x=8∴ x=8 and y=10

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