The mean heights of 3 groups of students consisting of 20, 16 and 14 students are 1.67m, 1.50m and 1.40m…

Concept: The combined mean is a weighted mean:

Combined mean = (sum of all heights) ÷ (total number of students)

The sum for each group is (group mean × number in group).

Step 1: Total height for each group

• Group 1: 20 × 1.67 = 33.4 m
• Group 2: 16 × 1.50 = 24.0 m
• Group 3: 14 × 1.40 = 19.6 m

Step 2: Add them up 33.4 + 24.0 + 19.6 = 77.0 m

Step 3: Total number of students 20 + 16 + 14 = 50

Step 4: Combined mean 77.0 ÷ 50 = 1.54 m

The mean height is 1.54 m, which is option C. (Option C is written without the "m" in the question, but the value is the same.)

Tip: For problems that combine groups, never just average the means. Always multiply each mean by its group size, add the results, then divide by the total number. Also, check that your answer lies between the smallest mean (1.40) and the largest (1.67), and closer to the means of the larger groups. Here 1.54 fits that check.