The mean height of 25 boys in a class is 150 cm, and the mean height of 35 girls in the same class is 145 cm. What is the approximate combined mean height of all 60 students in the class?

Introduction / Context:
This question illustrates a classic case of combining averages of two different groups into a single overall average. Boys and girls have different mean heights, and you are asked to find the combined mean height of the entire class. This is a typical weighted average problem in basic statistics and aptitude tests.

Given Data / Assumptions:

Number of boys = 25; their mean height = 150 cm.
Number of girls = 35; their mean height = 145 cm.
Total number of students = 25 + 35 = 60.
Heights are measured in centimetres.
We need the combined mean height of all 60 students, approximately.

Concept / Approach:
The combined mean height is found by dividing the total height of all students by the total number of students. To do this, we first find the total height of the boys from their mean and count, and similarly for the girls. Adding these totals gives the total height for the entire class. Dividing this by 60 yields the combined average height. Because the resulting value may not be an integer, we choose the closest option provided.

Step-by-Step Solution:
Step 1: Compute total height of the boys. Total height of boys = 25 * 150 = 3750 cm. Step 2: Compute total height of the girls. Total height of girls = 35 * 145 = 5075 cm. Step 3: Compute total height of all 60 students. Combined total height = 3750 + 5075 = 8825 cm. Step 4: Compute combined mean height. Combined mean height = 8825 / 60 ≈ 147.0833 cm. So the mean height is approximately 147 cm.

Verification / Alternative Check:
Notice that the boys' average (150 cm) is higher than the girls' average (145 cm), and there are more girls than boys. Therefore, the combined mean height must lie between 145 cm and 150 cm and closer to 145 cm but not too close, because 25 boys still influence the mean significantly. The approximate value 147 cm fits this reasoning and matches our calculation of 147.08 cm.

Why Other Options Are Wrong:
145 cm would be equal to the girls' average and would ignore the taller boys; with 25 boys at 150 cm average, the combined mean cannot be as low as 145.
143 cm is below both subgroup averages, which is impossible for a combined mean of only these two groups.
146 cm is slightly lower than the true value and does not match the precise weighted calculation, which is closer to 147 cm.

Common Pitfalls:
A common mistake is to take a simple average of 150 and 145, giving 147.5, without weighting by the different numbers of boys and girls. Others may miscalculate totals or divide by the wrong total number of students. Always multiply each group average by its group size, add those totals, and then divide by the combined group size to get the correct weighted mean.

Final Answer:
The combined mean height of all 60 students is approximately 147 cm.