Seventeen candidates appeared in an examination. The marks of the candidates who failed in the examination are 10, 9, 6, 7, 8, 8, 7, 5, 4, 6. The median of marks of all seventeen candidates is

The correct answer is C. With 17 candidates, the median is the 9th value once all marks are arranged in ascending order, so the position matters more than the average.

Arrange the failed candidates' marks: 4, 5, 6, 6, 7, 7, 8, 8, 9, 10. The 7 candidates who passed must have scored above every failed candidate, so their marks sit at the top of the full list. The first ten values are therefore the failed marks in order, and the 9th is 9.

• Option A (6): 6 occupies the 3rd and 4th positions, far below the median position.
• Option B (7): 7 occupies the 5th and 6th positions. This is the median only if you wrongly take the median of the 10 failed candidates alone.
• Option D: not needed, since 9 is correct.

The core concept is the median of ungrouped data: for n values, the median is the ((n+1)/2)th observation after sorting. This is basic descriptive statistics, and the same logic applies to cut-off and rank analysis in UPPSC-style data interpretation questions.

Trap: aspirants compute the median of only the 10 given marks (getting 7) and forget that the unknown passers, who score higher, shift the middle position.