A table of 50 observations has the class 40-50 with frequency 8. While forming $\sum f_i{x}_i$ the class mark of this class was taken as 40 instead of 45, and the mean came out as 33.2. What is the correct mean?

The slip made $\sum f_i{x}_i$ short by $8\times (45-40)=40$. The reported total was $33.2\times 50=1660$, so the correct total is 1700 and the correct mean is $\frac{1700}{50}=34$. The mean moves by $\frac{40}{50}=0.8$, not by 5. "38.2" adds the whole 5 to the mean; "41.2" adds the frequency 8; "33.2" assumes a wrong class mark leaves the mean unchanged.