The problem from the image states:

• The average age of 15 students is 15 years.
• Out of these, the average age of 5 students is 14 years.
• The average age of the other 9 students is 16 years.

We are asked to find the age of the 15th student.

Solution:

Let's break it down.

1. Total age of all 15 students: The average age of 15 students is 15 years, so the total age of all 15 students is: $\text{Total age of 15 students} = 15 \times 15 = 225 \text{ years}.$

2. Total age of 5 students: The average age of 5 students is 14 years, so the total age of these 5 students is: $\text{Total age of 5 students} = 14 \times 5 = 70 \text{ years}.$

3. Total age of 9 students: The average age of the other 9 students is 16 years, so the total age of these 9 students is: $\text{Total age of 9 students} = 16 \times 9 = 144 \text{ years}.$

4. Age of the 15th student: The sum of the ages of the 14 students (5 + 9) is: $\text{Total age of 14 students} = 70 + 144 = 214 \text{ years}.$ Therefore, the age of the 15th student is: $\text{Age of the 15th student} = 225 - 214 = 11 \text{ years}.$

So, the age of the 15th student is 11 years.

Would you like more details on any part of this problem?

Further related questions:

1. What is the meaning of "average" in a dataset?
2. How would the total age change if the average age of the 15 students were 16 years instead of 15?
3. How can you calculate the median age of these students?
4. What would happen if the age of the 15th student increased by 2 years? How would the overall average change?
5. If one student were removed, how would the calculation of the average change?

Tip:

When calculating averages, always make sure to multiply by the number of elements involved to get the total sum.