Section A has 30 students with an average of 60 marks and Section B has 20 students with an average of 70. What is the combined average?
64. Use a weighted average: (30 x 60 + 20 x 70) / 50 = (1,800 + 1,400) / 50 = 3,200 / 50 = 64. It is not 65, because the larger section pulls the average towards 60.
Explain it simply
Averaging two averages directly only works when the groups are the same size. Otherwise, each average must be weighted by how many people it represents. A good sense check: the combined average always lies between the two averages and closer to the bigger group.
Example
Question: A: 30 students, average 60. B: 20 students, average 70. Combined average?
- Total marks in A = 30 x 60 = 1,800.
- Total marks in B = 20 x 70 = 1,400.
- Combined = 3,200 / 50 = 64.
Alligation view: the groups are in the ratio 30 : 20 = 3 : 2, so the gap of 10 marks splits in the opposite ratio 2 : 3. The average sits 4 above 60 and 6 below 70. That is 64.
console.log((30 * 60 + 20 * 70) / (30 + 20)); // Output: 64The same idea gives the average price per kg when two qualities of rice are mixed, or a college's overall pass rate from department-wise rates.
What to say in the interview
"The sections are different sizes, so I weight each average by its count: 3,200 marks over 50 students gives 64. It is closer to 60 because section A is bigger."
Common mistakes
- Averaging the two averages to get 65.
- Weighting by the averages instead of the counts.