Question

Average grade of a section of \[20\] students is \[66\% \] and that of another section of \[15\]students is \[70\% \], what is the combined mean grade?

Answer 1

Hint: Always when we discuss the average then the first thing which we need to remember is the mean value of given data but it is not true for all because the average is the value that is equal to the sum of all given data and divided by the number of the data then we will get the average of that data.

Complete step by step Solution:
Given that –
Average grade of a section of \[20\]students is \[66\% \]
Now the total grade of a section of \[20\]students is $20 \times 66\% $
Now after multiplication, we will get
$ = 1320\% $
Again given that –
Average grade of a section of \[15\] students is \[70\% \]
Now the total grade of a section of \[15\]students is $15 \times 70\% $
Now after multiplication, we will get
$ = 1050\% $
Now the total number of students which is given in the question is the sum of a section of \[20\]students and a section of \[15\] students which is
$ = 20 + 15$
After addition, we will get the total number of students in the section which is
$ = 35$
Now the total grade of students is $1320\% + 1050\% = 2370\% $
And the total number of students in the section is $35$
Now the total average grade of the student in the section is equal to the sum of all grades and then we will divide it by the total number of students.
$ = $(total average grade) / (total number of students)
Now we will calculate it then we will get
$ = \dfrac{{2370\% }}{{35}}$
After calculating the value of the above divide, we will get the value of the total average grade of the students which is our desired value of our given question then we will get
$ = 67.71\% $.

So the combined mean grade of the student in the section is $67.71\% $.

Note:
The average is the value of the given data’s sum and divided by the number of data then we will get the value of the average of our given data and keep one thing in mind the total number of data and the multiplication of the given average is equal to the total sum of the number of the data.