The mean of 150 items was found to be 45. If at the time of calculation, two items were wrongly taken as 83 and 76 instead of 38 and 46, then the correct mean is:

Correct option is A

Given:
Mean of 150 item = 45
Formula Used:
Average = $$\frac{\text{ (Sum of elements)}}{\text{(Number of terms)}}$$​​
Solution:
Incorrect Sum = 150 $$\times$$​ 45 = 6750
Incorrect Values: 83 and 76
Correct Values: 38 and 46
Calculating the Difference:
Incorrect Sum - Correct Sum = (83+76) - (38+46) = 75
Calculating the Correct Mean:
Correct Sum = Incorrect Sum - Difference = 6750 - 75 = 6675
Correct Mean = $$\frac{\text{Correct Sum }}{\text{ Number of terms }}$$​= $$\frac{6675}{ 150}$$​ = 44.5
Correct mean is: 44.5