The marks out of 50 obtained by 100 students in a test are given below as:
| Marks obtained | 20 | 25 | 28 | 29 | 33 | 38 | 42 | 43 |
| Number of students | 6 | 20 | 24 | 28 | 15 | 4 | 2 | 1 |
Find the value of the (3 mode - 2 median).
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 30
The mode is the value with the highest frequency. The median is the middle value; for 100 students it is the average of the 50th and 51st values, which the cumulative frequencies locate.
The largest group, 28 students, scored 29 marks, so mode \(=29\)
Cumulative frequencies: 20 marks 6, 25 marks 26, 28 marks 50, 29 marks 78, and so on
The count reaches 50 at 28 marks, so the 50th student scored 28; students 51 to 78 scored 29, so the 51st scored 29
Median \(\displaystyle =\frac{28+29}{2}=28.5\)
\(3\times\text{mode}-2\times\text{median}=3\times29-2\times28.5=87-57=30\)
Tip: Here the 50th and 51st values differ, so both are needed for the median. Taking only the 50th value (28) gives 31, which is Option (2).