Question

a.       Two sections of a class took the same quiz. Section A had 16 students who had a mean score of 84, and section B had 20 students who had a mean score of 90. Overall, what was the mean score for all students who took the quiz from sections A and B?

b.       A professor has recorded quiz grades for 20 students in his class, but one of the grades is no longer readable. If the mean score on the quiz was 80 and the mean of the 19 readable scores is 82, what is the value of the unreadable score?   

Answer 1

a) We have the number of students in section A as, n = 16 and the mean of section A be,

Also the number of students in section B is known to be, m = 20 and the mean of section B is given by,

Then the mean score of all students or the pooled mean is given by,

Hence we have the pooled mean as

Also here

are sum of marks of students Section A and Section and m+n is the total number of students.

b)

We are given that mean for 20 students is 80 and mean for 19 students is 82.

The total sum of the score of 19 students is equal to, 82*19 = 1558 because

Then, (1558 + unreadable score) / 20 = 80

1558 + unreadable score = 80*20 =1600

unreadable score = 1600 - 1558 = 42.