Question

The mean weight of $98$ students is found to be $50$ lbs. It is later discovered that the frequency of the class interval $(30-40)$ was wrongly taken as $8$ instead of $10$. Calculate the correct mean.

• A. $49.00$
• B. $49.50$
• C. $49.25$
• D. $49.70$

Answer 1

The correct option is D $49.70$

Incorrect mean,
$X=50$kg.
$\sum f_i=98$
Incorrect X$=\frac{Incorrect\sum f_i{X}_i}{\sum f_i}$
$50=\frac{Incorrect\sum f_i{X}_i}{98}$
$\therefore$ Incorrect $\sum f_i{X}_i=98\times 50=4900$
Now, Correct $\sum f_i{X}_i=$Incorrect $\sum f_i{X}_i-(8\times 35)+(10\times 35)$
Note, the class-mark of class interval $(30-40)$ is $35$ and for the calculation of the mean, we consider class marks.
Correct $\sum f_i{X}_i=4900-280+350$
$=4,970$
Also, Correct $\sum f_i=98+2=100$
$\therefore$ Correct Mean$=\frac{Correct\sum f_i{X}_i}{Correct\sum f_i}$
$=\frac{4970}{100}$
$X=49.70$lbs.