Question

The mean of 53 observations is 35 and out of them three observations are 80, 30 and 60. If we exclude these three observations, then the mean is equal to

• A. 40
• B. 33.7
• C. 37
• D. 36

Answer 1

The correct option is B 33.7

Let $x_1,x_2,......,x_{53}$ be 53 observations such that their mean is 35.

$Mean=\frac{Sumofobservations}{Totalnumberofobservations}$

$\Rightarrow 35=\frac{x_1+x_2+...+x_{52}+x_{53}}{53}$
$\Rightarrow 35=\frac{{\sum }_{i=1}^{53}{x}_i}{53}$
$\Rightarrow {\sum }_{i=1}^{53}{x}_i=35\times 53=1855$....(i)

Let the three observations $x_{51},x_{52}$ and $x_{53}$ be 80, 30 and 60 respectively.

$\therefore {\sum }_{i=1}^{50}{x}_1+x_{51}+x_{52}+x_{53}=1855$ [From (i)]

$\Rightarrow {\sum }_{i=1}^{50}{x}_1+80+30+60=1855$

$\Rightarrow {\sum }_{i=1}^{50}{x}_1=1855-170=1685$....(ii)
$\therefore$
Mean of the remaining 50 observations = $\frac{{\sum }_{i=1}^{50}{x}_i}{50}$

$=\frac{1685}{50}$ [from (ii)]

$=33.7$
Hence, the correct answer is option b.