Critical Reasoning

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Thanks everyone!

Set X and Y have 10 numbers, respectively. Is standard deviation of X greater than that of Y?

1) Range of X is greater than than of Y

2) Average of X is greater than that of Y

This is a data sufficiency Question.

Correct answer is : E

This is a question from their topic Statistics, Please help explain how it is Option E?

This is a stats question and would normally be in the Quant Data Sufficieny Forum, but I can answer it since it is here.

The question is asking you to compare the standard deviation of two sets.

If you have 3 things you will know for sure which standard deviation is bigger.

1) You need to know that the sets have the same number of terms. This is very important. Without this step you could have one set with 2 terms and the other with 200 terms.

2) You need to know that each set is somehow uniformly spaced or have some way to compare the spacing. This is what is missing in this question. Without this information, even though each set has ten terms and even though statement 1 tells you that set x has a larger range, there is no way of knowing if set x has the larger deviation. Set x might have the terms 1 55555555 10 and set Y might have the terms 22222 10 10 10 10 10. You can see that set X has the greater range, but set Y surely has the greater deviation.

3) If you have the same number of terms and uniform spacing you just need to know which one has the larger range. We have this information but as stated above it is not enough.


Also note that statement 2 is useless. When speaking of standard deviation what matters is the spacing or variance of the numbers, not the actual values of those numbers. Unless we knew that each set started at the same number or something this information is of no value to this question.

Statement 1 is not sufficient. Statement 2 is not helpful. The answer is E.

Does that help?

That clarified my doubt completely, thanks a ton!