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Q.

If the standard deviation of 10 observations x1,x2,.....,x10 is 4 and that of another set of 10 observations y1,y2,.......y10 is 3 and also Xi=xix¯yiy¯x¯ is mean of all  xi’s and  y¯ is mean all  yi’s  and  i=110Xi=80. Then standard deviation of observations x1y1,x2y2,......,x10y10 is

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a

1

b

5

c

3

d

5

answer is B.

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Detailed Solution

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i=110xix¯yiy¯=80

i=110xiyiyi=110xixi=110yi+i=110xy=80 which implies 

i=110xiyi10yx=80, σ2=i=110xiyi210y¯x¯2=9

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