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Students taking an exam are divided into two groups, P and Q such that each group has the same number of students. The performance of each of the students in a test was evaluated out of 200 marks. It was observed that the mean of group P was 105, while that of group Q was 85. The standard deviation of group P was 25, while that of group Q was 5. Assuming that the marks were distributed on a normal distribution, which of the following statements will have the highest probability of being TRUE?

Students taking an exam are divided into two groups, P and Q such that each group has the same number of students. The performance of each of the students in a test was evaluated out of 200 marks. It was observed that the mean of group P was 105, while that of group Q was 85. The standard deviation of group P was 25, while that of group Q was 5. Assuming that the marks were distributed on a normal distribution, which of the following statements will have the highest probability of being TRUE? Correct Answer Most students of group Q scored marks in a narrower range than students in group P.

Standard Deviation is a measure that is used to quantify the amount of variation or dispersion of a set of data values.

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For P, SD = 25 and m = 105

So the limits will be m – 2s = 55 and m + 2s = 155

For Q, SD = 5 and m = 85

So the limits will be m – 2s = 75 and m + 2s = 95

95% of students in P scores between 55 to 155.

95% of students in Q score between 75 to 95.

For Normal Distribution: Mean = Median = Mode. D is not correct.

A and B cannot be said to be true with certainty.

C is the correct answer. As the SD of Q is less than P, most students of group Q scored marks in a narrower range than students in group P.

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