
Shortcut Trick
Assume the base average score is 70.
Deviation for the first 12 students = 12 × (80 − 70) = +120.
Distributed deviation for all 30 students = 120 ÷ 30 = 4.
Total average score = Base average + Deviation = 70 + 4 = 74.
∴ The correct answer is 74.

Alternate Method
Given:
Total number of students = 30
Number of students in the first group = 12
Average score of the first group = 80
Number of students in the second group = 30 − 12 = 18
Average score of the second group = 70
Formula Used:
Combined Average = Total Sum of Scores ÷ Total Number of Students

Calculations:
⇒ Total score of 12 students = 12 × 80 = 960
⇒ Total score of the remaining 18 students = 18 × 70 = 1260
⇒ Total score of the whole class = 960 + 1260 = 2220
⇒ Average score of 30 students = 2220 ÷ 30
⇒ Average score = 74
∴ The correct answer is 74.

Additional Information
Combined Mean Formula
The combined mean (xc) of two groups is calculated as: xc = (n1x1 + n2x2) ÷ (n1 + n2), where n is the size and x is the average of each group.
Weighted Average
Used when items in a data set have different levels of importance or frequency; each value is multiplied by its weight before summing and dividing by the total weight.
Deviation Method
A mental math technique where an assumed mean is used, and the net deviation from this mean is adjusted across the total count to find the actual average.