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Let a , b , c N and a < b < c . Let the mean, the mean deviation about the mean and the variance of the 5 observations 9,25, a , b , c be 18,4 and 136 5 , respectively. Then 2 a + b - c is equal to__________

Correct answer

0

Step-by-step solution

a, b, c N a < b < c x = mean = 9+25+ a + b + c 5 =18a+b+c=56 Mean deviation = | x _ i - x | n =4 aligned & =9+7+|18- a |+|18- b |+|18- c |=20 & =|18- a |+|18- b |+|18- c |=4 aligned Variance = | x _ i - x |^2 n = 136 5 aligned & =81+49+|18-a|^2+|18-b|^2+|18-c|^2=136 & =(18-a)^2+(18-b)^2+(18-c)^2=6 aligned Possible values (18- a )^2=1, (18- b )^2=1 (18- c )^2=4 a < b < c so array ccc 18-a=1 & 18-b=-1 & 18-c=-2 a =17 & ~b =19 & c =20 array a+b+c=562 a + b - c 34=19-20=33

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