Question

The image shows distribution of marks secured by 2500 students of a particular district in four subjects. Which of the statements must be TRUE?

• A. If 50 marks are required for passing, more students will fail in English than in Hindi
• B. If 75 marks are required for securing a distinction, most distinctions will be awarded in English
• C. The average marks secured in Science is highest compared to other subjects
• D. Students have performed more uniformly in Maths than in any other subject

Hint:

In a normal distribution graph: the peak's location on the x-axis gives the average (mean), and the curve's width indicates the data's spread. A narrow curve means uniform data (low standard deviation), while a wide curve means diverse data (high standard deviation).

Answer 1

The Correct Option is A, D

1. Option A: English's curve sits closer to the 50-mark cutoff than Hindi's, so more students fail English, making this correct.
2. Option B: The 75-mark cutoff falls in a thinner part of English's curve than it does for the higher-scoring subjects, so distinctions are not concentrated in English, making this incorrect.
3. Option C: Another subject's curve peaks higher than Science's, so Science does not have the top average, making this incorrect.
4. Option D: Maths has the narrowest curve of the four, meaning scores are most tightly clustered there, making this correct.

A and D are correct.

Answer 2

A quick way to work through this set is to first pick out the two extreme curves — the one with the highest peak and the one that is narrowest — since two of the four statements are really about those extremes.

1. Option D: The narrowest curve, the one where scores are packed most tightly around its average, belongs to Maths, which directly means Maths shows the most uniform performance. True.
2. Option C: The highest peak, however, belongs to a different subject than Science, so the claim that Science has the top average does not hold. False.
3. Option A: Once the extremes are set aside, comparing English and Hindi shows English's curve sitting nearer the 50-mark cutoff, so a bigger share of English students falls below it than Hindi students. True.
4. Option B: Since English is also the widest, flattest curve of the four, very few of its students reach as far out as the 75-mark distinction line compared to the more sharply peaked subjects, so distinctions are not concentrated there. False.

Working from the extremes inward still lands on the same two true statements.

So the correct answer is A and D.