Carcass wrote:
On a certain exam, the median grade for a group of 25 students is 67. If the highest grade on the exam is 90, which of the following could be the number of students that scored 67 on the exam?
Indicate all such values.
A. 5
B. 20
C. 24
We have 25 students in a group, so grade of \(13^{th}\) student should be the Median of the group
|- - - - - - - - - - - - M(67) - - - - - - - - - - - -|
i.e. we have 12 students to the left of M and 12 students to the right of M
Now, Highest grade is 90
|- - - - - - - - - - - - M(67) - - - - - - - - - - - 90|
Let's check the option choices;
I. 5 students have a score of 67
|- - - - - - - - - - (67) (67) (M) (67) (67) - - - - - - - - - 90|
II. 20 students have a score of 67
|- - (67) (67) (67) (67) (67) (67) (67) (67) (67) (67) (M) (67) (67) (67) (67) (67) (67) (67) (67) (67) - - 90|
III. 24 students have a score of 67
|(67) (67) (67) (67) (67) (67) (67) (67) (67) (67) (67) (67) (M) (67) (67) (67) (67) (67) (67) (67) (67) (67) (67) (67) 90|