Question

There are 40 female and 20 male students in a class. If the average heights of female and male students are 5.15 feet and 5.66 feet, respectively, then the average height (in feet) of all the students in the class equals:

• A. 5.490
• B. 5.405
• C. 5.175
• D. 5.320

Hint:

For weighted averages, multiply each value by its weight (number of students) and then divide by the total number of students.

Answer 1

The Correct Option is D

Step 1: Use the weighted average formula.
To find the average height of all students, we calculate the weighted average of the female and male heights, based on their respective numbers. The formula for weighted average is: \[ \text{Average height} = \frac{(40 \times 5.15) + (20 \times 5.66)}{40 + 20}. \]

Step 2: Compute the average.
\[ \text{Average height} = \frac{(206) + (113.2)}{60} = \frac{319.2}{60} = 5.320. \]

Step 3: Conclusion.
Thus, the average height of all students is 5.320 feet, and the correct answer is (d).