Discussion

Marks	3	4	5	6	7	8	9
Frequency	3	9	11	7	14	2	4

The above frequency chart shows the frequency distribution of marks obtained by a set of students in an exam.

From the data presented above, which one of the following is CORRECT?

Answer: B

The correct order is mode \(\gt\) median \(\gt\) mean.

There are \(3 + 9 + 11 + 7 + 14 + 2 + 4 = 50\) students.

Mode: the highest frequency, 14, is at 7 marks.
Median: the 25th and 26th values. Cumulative frequencies are 3, 12, 23, 30, ..., so both fall at 6 marks: median 6.
Mean: \((9 + 36 + 55 + 42 + 98 + 16 + 36)/50 = 292/50 = 5.84\).

So 7 \(\gt\) 6 \(\gt\) 5.84. The other options put the mean above the median or the median above the mode, which these numbers contradict.

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