Answer:
The average of the whole class is 80.8.
The correct answer is B)
Step-by-step explanation:
To solve this problem, it is very important to understand the phrase: "Ten students had an average of 88". Let's see an example.
Imagine that three students in the class took a test and their scores were: 80, 89 and 95. To calculate the average of they three we must divide the sum of the scores by the total number of scores.
[tex]average=\frac{80+89+95}{3}=\frac{264}{3}=88[/tex]
The previous value is the average of the three students. Now, if we say that each student got 88, the average would be 88.
[tex]average=\frac{88+88+88}{3}=\frac{264}{3}=88[/tex]
The previous expression could be simplified as:
[tex]average=\frac{88\times 3}{3}[/tex]
Where, the number 3 means the number of students.
With that in mind, the phrase "Ten students had an average of 88" could be written as:
[tex]average_{10\, \, students}=\frac{88+88+88+88+88+88+88+88+88+88}{10}[/tex]
[tex]average_{10\, \, students}=\frac{88\times 10}{10}=88[/tex]
On the other hand, the phrase "The other students had an average of 76" means that from the 25 students, 15 students got 76 (25 - 10 = 15), and could be written as:
[tex]average_{15\, \, students}=\frac{76+76+76+76+76+76+76+76+76+76+76+76+76+76+76}{15}[/tex]
[tex]average_{15\, \, students}=\frac{76\times 15}{15}=76[/tex]
Finally, to calculate the total average of the 25 students we must divide the sum of the scores of all students by the total number of scores. The sum would be: 88+88+88+88+88+88+88+88+88+88+76+76+76+76+76+76+76+76+76+76+76+76+76+76+76, which equals [tex]88\times 10+76\times 15[/tex]. The total number of scores would be: 25.
[tex]average_{total}=\frac{88\times 10 + 76\times 15}{25}[/tex]
[tex]average_{total}=\frac{880 + 1140}{25}[/tex]
[tex]average_{total}=\frac{880 + 1140}{25}[/tex]
[tex]average_{total}=\frac{2020}{25}[/tex]
[tex]average_{total}=80.8[/tex]
Thus, the average of the whole class is 80.8. The correct answer is B)
