Kaplan GMAT Challenge Question: Standard Deviation
Data Sufficiency Question:
For a certain exam, was the standard deviation of the scores for students U, V, W, X, Y and Z less than the standard deviation of the scores for students A, B and C?
(1) The standard deviation of the scores of students U, V, and W was less than the standard deviation of the scores of students A, B and C on the exam.
(2) The standard deviation of the scores of students X, Y and Z was less than the standard deviation of the scores of students A, B and C on the exam.
Remember that standard deviation is a measurement of how spread-out a set of numbers are around the mean. As is usually the case on the GMAT, this problem does not require us to calculate standard deviation. Rather, we just need to understand the CONCEPT of standard deviation.
Statement 1 tells us that U, V and W have a lower standard deviation that A, B and C. However, this tells us nothing about X, Y and Z. Without knowing all of the numbers in the set, you are unable to calculate standard deviation. Statement 1 is, therefore, insufficient.
Statement 2 tells us that X, Y and Z is smaller than the standard deviation of A, B and C. Now, we do not know anything about U, V and W. For the same reasons as in statement 1, statement 2 is not sufficient.
When the statements are considered together, we know that the sets U, V and W and X, Y and Z both have a standard deviation that is less than the set of A, B and C. However, we do not know the relationship between the two former sets. It is possible that U, V, W, X, Y and Z are all closer together than A, B and C are, but it is also possible that the sets U, V and W and X, Y and Z are so far apart from each other that the overall set ends up having a larger standard deviation than the set A, B and C. Therefore, together the statements are still insufficient; answer choice (E) or (5)—not enough information here to answer the question.
Even though this appears to be a challenging problem on first glance, including data sufficiency and standard deviation, we did not have to use our scratch paper necessarily or compute any actual mathematical calculations….sometimes questions on test day will be more focused on your conceptual understanding, and instead of becoming overwhelmed when you see words like “standard deviation”, you should stay calm, read carefully, and remind yourself of the concepts you do know as you analyze the question.