The average marks of 50 students in a class was found to be 64. If the marks of two students were incorrectly entered as 38 and 42 instead of 83 and 24, respectively, then what is the correct average?

Given,A

Average of 50 students in a class = 64

Marks of two members were wrongly copied as 38 and 42 instead of 83 and 24.

Mean = $$\frac{\text{Sum of all observations}}{\text{Number of Observations}}$$

let the sum of all observations be x

According to the problem,

64 = $$\frac{x}{50}$$

$$64×50$$ = $$x$$

$$x$$ = 3200

Subtract the wrongly copied numbers from the total sum

= $$3200 - (38+42)$$

= $$3200 - 80$$

= $$3120$$

Now add the new numbers to the total sum

= $$3120 + (83+24)$$

= 3227

Thus, new sum is 3227

New Mean = $$\frac{3227}{50}$$ = 64.54

Therefore, new Mean = 64.54