Classroom Statistics
Probability
Level
1
A class of 30 students took a test, and the mode of their test scores is 85. If another student who took the same test enters the class, will the mode still be 85?
No, never
It is possible, but not guaranteed
Yes, always
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1 solution
If I understand the question correctly, it asks whether the most common score (85 marks) achieved by the students (present) in a class(room) will stay the same or not if a new student enters the class(room).
The answer is possible, but cannot be guaranteed, because:
Possible, for instance in the following case:
3 students achieved 85 marks, each of the other 27 students have different (unique) scores (both from each other and from 85 marks, in other words, their scores have a frequency of 1). If a new student enters in the classroom, whatever his/her score is, it cannot make another score more frequent than 85, as in the worst case, only 2 students will share the other score.
Cannot be guaranteed:
If 3 students have 85 marks, 2 students 86 marks (scores of the other 25 students are unique) and the new student has 86 marks, then we have two most common scores (2 modes: 85 and 86), therefore we cannot say that only 85 is the most common score (it is now just one of the two).