In a class the average age of the boys is 16 years and the average age of the girls is 15 years. What is the average age of the whole class?

Introduction:
This question is about understanding when average information is sufficient and when it is not. We are given the average ages of boys and girls separately and asked to find the average age of the entire class. The key issue is whether we know how many boys and how many girls there are.

Given Data / Assumptions:
- Average age of boys = 16 years. - Average age of girls = 15 years. - The numbers of boys and girls are not given. - We want the average age of all students in the class.

Concept / Approach:
The average of the whole class is a weighted average of the average age of boys and the average age of girls. The weights are the numbers of boys and girls. Without knowing at least the ratio between the number of boys and the number of girls, we cannot compute a unique value for the overall average.

Step-by-Step Reasoning:
Step 1: Let the number of boys be b and the number of girls be g. Step 2: Total age of boys = 16b. Step 3: Total age of girls = 15g. Step 4: Total students = b + g, and total age = 16b + 15g. Step 5: Average age of the whole class = (16b + 15g) / (b + g). Step 6: This expression depends on the unknown values b and g. Without a relation between b and g, the result is not a single fixed number. Step 7: For example, if b = g, the average would be (16 + 15) / 2 = 15.5 years, but if there are many more boys than girls, the overall average would be closer to 16 years, and if there are many more girls the overall average would be closer to 15 years.

Verification / Alternative Check:
Choose specific cases to see the variation. If there are 10 boys and 10 girls, average = (16*10 + 15*10) / 20 = (160 + 150) / 20 = 310 / 20 = 15.5 years. If there are 20 boys and 10 girls, average = (16*20 + 15*10) / 30 = (320 + 150) / 30 = 470 / 30 which is approximately 15.67 years. These examples show that the answer changes with the composition of the class.

Why Other Options Are Wrong:
Option 15, 15.2, 15.5 and 15.8 each assume a particular ratio of boys to girls. Since that ratio is not given, none of these numerical values can be guaranteed to be correct.

Common Pitfalls:
A very common error is to directly average 16 and 15 and declare 15.5 as the answer. This only works when the numbers of boys and girls are equal. In general, when you are given the averages of subgroups, you must know the subgroup sizes to find the overall average.

Final Answer:
The information is insufficient; the correct choice is data inadequate.