Question

The mean of $20$ observations is $15$. One observation, $20$ is deleted and two more observations are included to the data. If the mean of new set of observations is $15$, then find the sum of the two new observations included.

• A. $30$
• B. $35$
• C. $33$
• D. $32$

Answer 1

The correct option is B $35$

Answer:-

Given:- Mean of 20 observations is 15.

$\therefore \text{sum of 20 observations}=mean\times 20=15\times 20=300$

In the sum one observation is deleted .

$\therefore \text{Sum of 19 observations}=300-20=280$

Let the sum of two observations be x that will be added to the given observation.

Sum of 21 observation = sum of 19 observations + Sum of 2 observations = 280 + x

Now, New mean = $\frac{\text{Sum of 21 observations}}{21}=\frac{280+x}{21}$

But mean is 15

$\Rightarrow \frac{280+x}{21}=15$

$\Rightarrow 280+x=315$

$\Rightarrow x=35$

B) 35