Question

Suppose that one a guiz given to 7 students, the maximum score was 15. (a) If the median score was 10, what is the highest possible mean? the lowest? (b) If the mean score was 10, what is the largest possible number of students who could have received 0 points on the quiz? (c) If the mode of the set of scores was 15, what is the largest possible median? how about the largest possible mean?

Answer 1

(a) highest possible =15 and lowest =0

since median score is 10 it means 4th student will get 10 marks out be 7 if arranged in ascending (or descending )order.

so minimum score 0 and maximum score 15 possible e.g. 0,4,6,10,12,13,15 ( this is one of the case out of many cases)

(b)answer is 2

mean is 10 means total marks of the student will be =10*7=70

if four student get 15 marks and one student 10 marks, then total 70 marks from the 5 student.

so maximum/largest 2 student get 0 marks

(c) largest possible median=15 and largest possible mean=15

if all the student will get 15 marks, then mode will be 15, so median and mean will also be 15 .