College P has 180 students scoring average marks of 88 and college Q has 320 students scoring average marks of 72. Find the average marks of both the colleges together.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 77.76.
Given that
Average marks of 180 students in college P = 88
Average marks of 320 students in college Q = 72
Average = sum of observations / total number of observations
⇒ 88 =
⇒ 88 × 180 = sum of marks of students in P
⇒ sum of marks of students in P = 15840
Also,
72 =
⇒ sum of marks of students in Q = 23040
Total sum = 15840 + 23040 = 38880
Combined average = = 77.76