Study the following table and answer the questions. Classification of 100…
2024
Study the following table and answer the questions. Classification of 100 Students Based on the Marks Obtained by them in Physics and Chemistry in an Examination.
The number of students scoring less than 40% marks in aggregate is?
- A.
13
- B.
19
- C.
20
- D.
27
Attempted by 2 students.
Show answer & explanation
Correct answer: D
Concept: In a table with 'at least / X and above' cumulative frequencies, the number of students scoring below a given marks cutoff equals the total number of students minus the cumulative count for that cutoff. To convert a percentage cutoff into a marks cutoff, multiply the percentage by the maximum marks.
40% of the maximum 50 marks = (40/100) × 50 = 20 marks — this is the marks cutoff the question refers to.
From the 'Average (Aggregate)' row of the table, the cumulative count for '20 and above' is 73 — so 73 students scored 20 marks or more in aggregate.
Since there are 100 students in all, the number scoring less than 20 marks (i.e., less than 40%) = 100 − 73 = 27.
Cross-check: As an independent check, split the 100 students into non-overlapping mark-bands using successive differences of the aggregate row: below 10 marks = 100 − 87 = 13; 10 to 19 marks = 87 − 73 = 14; 20 to 29 marks = 73 − 27 = 46; 30 to 39 marks = 27 − 7 = 20; and 40 marks and above = 7. These five bands add up to 13 + 14 + 46 + 20 + 7 = 100, confirming the table is internally consistent, and the below-20-marks total (the first two bands) = 13 + 14 = 27, matching the result obtained above.