Question

C 17. At high school A, the mean score of 50 students on a science test is 75.
At high school B, the mean score of 40 students on the same test is 80.
What is the mean score of the 90 students?

Answer 1

Answer:

Mean score of 90 students = 77.2

Step-by-step explanation:

Mean score of 50 students from school A = 75

Mean score of 40 students from school B = 80

We need to find mean score of the 90 students?

First we will find sum of scores of students from school A

We know that: $Average=\frac{Sum\:of\:Terms}{Number\:of\:terms}$

We have Average = 75, Number of terms = 50, We need to find Sum of terms (scores)

$Average=\frac{Sum\:of\:Terms}{Number\:of\:terms}\\75=\frac{Sum\:of\:Terms}{50}\\Sum\:of\:Terms= 75\times 50\\Sum\:of\:Terms=3750$

So, Sum of scores for School A = 3750

Now, we will find sum of scores of students from school B

We know that: $Average=\frac{Sum\:of\:Terms}{Number\:of\:terms}$

We have Average = 80, Number of terms = 40, We need to find Sum of terms (scores)

$Average=\frac{Sum\:of\:Terms}{Number\:of\:terms}\\80=\frac{Sum\:of\:Terms}{40}\\Sum\:of\:Terms= 80\times 40\\Sum\:of\:Terms=3200$

So, Sum of scores for School B = 3200

Now, We will find mean score of the 90 students?

Mean score of 90 students will be:

$Average=\frac{Sum\:of\:Terms}{Number\:of\:terms}\\Average=\frac{3750+3200}{90}\\Average=\frac{6950}{90}\\Average = 77.2$

So, mean score of 90 students = 77.2