The mean and the standard deviation S.D. of five observations are 9 and 0, respectively. If one of the observation is increased such that the mean of…

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The mean and the standard deviation S.D. of five observations are 9 and 0, respectively. If one of the observation is increased such that the mean of the new set of five observations becomes 10, then their S.D. is

MARKS Content Team · Accepted Answer

Correct answer: (B) 2. x¯=(∑x_i)/n=9 s.d=√(∑xi-x¯^2n)=0 ⇒x_i=x¯∀i ∴ each term in the original observation is 9 ⇒ observation 1={9,9,9,9,9} x¯_(new )=(∑x_i)/n=(9+9+9+9+x_5)/5 ⇒10=(36+x_5)/5 ⇒x_5=14 ⇒ new set of observations ={9,9,9,9,14} s.d_(new )=√(∑xi-x¯new^2n) =√((9-10)^2+(9-10)^2+(9-10)^2+(14-10)^25) =√(4+4^25) =√205=2

The mean and the standard deviation $(S . D .)$ of five observations are $9$ and $0$ , respectively. If one of the observation is increased such that the mean of the new set of five observations becomes $10$ , then their $S . D .$ is

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