In a class of 50, the average height of 30 boys is 160 cm. The remaining students have an average height of 165 cm. What is the average height of the whole class (in cm)?

Introduction:
This is a weighted-average calculation across two subgroups. Convert each subgroup's average to a total, add, and divide by the total headcount to find the overall average.

Given Data / Assumptions:
Total students = 50. Group 1: 30 at 160 cm. Group 2: 20 at 165 cm (the remaining students).

Concept / Approach:
Overall average = (Sum of subgroup totals) / 50. Subgroup totals are count * average for each group.

Step-by-Step Solution:
Total height group 1 = 30 * 160 = 4800 cm. Total height group 2 = 20 * 165 = 3300 cm. Total height overall = 4800 + 3300 = 8100 cm. Overall average = 8100 / 50 = 162 cm.

Verification / Alternative check:
Weighted average view: (30/50)*160 + (20/50)*165 = 96 + 66 = 162, which matches.

Why Other Options Are Wrong:
161, 163, 164, 160: Do not equal the computed weighted average.

Common Pitfalls:
Averaging 160 and 165 directly to get 162.5 without considering group sizes; correct method uses weights 30 and 20.

Final Answer:
The class average height is 162 cm.