It's a normal question with two gists: equally spaced difference between each value and mean, and one important concept that follows. The closer a value is to the mean, the higher its percentile (data concentration) around the mean.

If there's not a 6-point difference between values, but say only one-point equally spaced difference such as mean score = 72, two other scores are 73 and 74, then the percentile of 73 score > the percentile of 74 score.

good question and query is that by any Chance SD is 6 because in question there is not such explicitly mentioned.

How come percentile of 73 > percentile of 73?

However, the area under the curve (number of values) between 72 and 73 > area under the curve (number of values) between 73 and 74.

Please correct me if I am wrong.

Closer to the mean = More area = Higher Probability of Data distribution under that region.
Away from the mean = Less area = Lower Probability of Data distribution under that region.

Before you even start solving look at Quantity A & B. It's dealing with "Percentiles" not "Standard Deviation" !! So keep that in mind.

The Data of the 50th percentile is = 72. (Given)

The Data of the nth percentile is = 78. (6 units away from the mean) (Given) We can deduct from this statement that the nth percentile is smaller than the 50th percentile cuz we know from the bell curve more we deviate from the mean the more the Probability of the data falling under that area decreases. That's why it goes like 50% 34% 14% 2%.

The Data of the mth percentile is = 84. (12 units away from the mean) (Given) We can deduct from this statement that the mth percentile is smaller than the nth percentile cuz we know from the bell curve more we deviate from the mean the more the Probability of the data falling under that area decreases. That's why it goes like 50% 34% 14% 2%.


The twist is in the question (not in the prompt). Are we asked to find in terms of standard deviation? Nah !! That's not even mentioned. We don't know that. So we can't just do quantity A: 34%+14% and stuff like that. Cuz we don't know the SD at all !! And thus it could happen that we are dealing with all these within 1 SD. :O

Now we're ready to tackle this. As we have seen n is smaller than the 50th percentile so n is less than 50. Suppose n=40.
So Quant A: 40-50=-10
And we have already seen that m is half of the 50th percentile compared to n. Thus m=20.

Quant B: 20-40=-20
Quant A Greater.

Thanks for the reply. I often get confused with percentile question.
a. Could you kindly clarify that for normal distributions and percentiles, is it necessary to have 100 unique data points (or bins as in histogram). For example, can we have a normal distribution for a test with obtained scores between 72 and 76 for say 500 students.
b. Can we have a normal distribution for case A and case B?

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