The mean and standard deviation of 100 observations are 40 and 5.1, respectively. By mistake one observation is taken as 50 instead of 40. If the correct mean and the correct standard deviation are a…

Question

The mean and standard deviation of 100 observations are 40 and 5.1, respectively. By mistake one observation is taken as 50 instead of 40. If the correct mean and the correct standard deviation are and respectively, then 10 ( + ) is equal to

Accepted Answer

Correct answer: C. (c) Let the observations be x_1 ,x_2 , … ,x_99 ,50 Mean= x_1+x_2+ …+x_9+50100=40 ⇒x_1+x_2+ …+x_99=4000-50 ⇒x_1+x_2+ …+x_99=3950 Current Mean= 3950+40100 = 39910=39.9 (S .D )^2= 0.05em 0.05em (x_i )^2+2500100- (40 )^2 0.05em 0.05emx_i^2=160101 ( CorrectS .D )^2= 160101+1600100- ( 39910 )^2 =510 ( + )=10 (39.9+5 )=449

$The mean and standard deviation of 100 observations are 40 and 5.1, respectively. By mistake one observation is taken as 50 instead of 40. If the correct mean and the correct standard deviation are μ and σ respectively, then 10 (μ + σ) is equal to$

Solution

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