Question

The mean of a certain number of observations is $35$. What is the new value of the mean if each observation is increased by $20\%$.

• A. $35$
• B. $40$
• C. $42$
• D. None of these

Answer 1

The correct option is C $42$

Let the count of observations is $N$

Mean $=\frac{\text{Sum ofd observations}}{N}=35$ ....Given

Let the observations be $x_1,x_2,x_3,......,x_N$

Sum of observations $=\sum x_1+x_2+x_3+......+x_N=35N$

If each observation is increased by $20$ percent, then

New sum of observations $=\sum x_1+x_1\times 0.2+x_2+x_2\times 0.2+x_3+x_3\times 0.2+......+x_N+x_N\times 0.2$

$=$ sum $x_1+x_2+x_3+......+x_N+0.2\sum x_1+x_2+x_3+......+x_N$

$=(1+0.2)\sum x_1+x_2+x_3+......+x_N$

$=1.2\times 35N=42.0\times N=42N$

New Mean $=\frac{42N}{N}=42$