Weighted average of two subgroups: In a class of 40 girls, the average height of 30 girls is 160 cm and the average height of the remaining 10 girls is 156 cm. Find the overall average height of the class.

Introduction / Context:
This is a weighted average scenario: two groups have different averages and sizes. The overall average depends on both group means and their counts.

Given Data / Assumptions:

• Total students = 40
• Group 1: 30 girls, average 160 cm
• Group 2: 10 girls, average 156 cm

Concept / Approach:
Overall average = (sum of group totals) / total count. Compute each group total by mean * size and add them.

Step-by-Step Solution:

Verification / Alternative check:
Since the larger group average (160) is above the smaller group average (156), the final average should be between 156 and 160 and closer to 160, that is 159.

Why Other Options Are Wrong:

• 158.5, 157: too low relative to the 30 at 160.
• 160, 161: do not account for the lower subgroup mean at 156.

Common Pitfalls:
Using plain mean of 160 and 156 without weighting by group sizes. Weighted totals are essential.

Final Answer:
159 cm