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Since the SD of any set is less than or equal to the range, here SD is less than or equal to 4. 5 cases. But since SD cannot be 0, answer is 4.
Is this the right way to approach this?
Is this the right way to approach this?
Gmat232323
No, that wouldn’t be a correct way of solving this. You are assuming that the standard deviation could only take integer values, so you thought it must be 0, 1, 2, 3, or 4, then ruled out 0 and concluded there are 4 possibilities. But that logic doesn’t hold, the standard deviation does not have to be an integer.
What the question is really asking is: given the constraints (four odd integers, maximum difference of 4), how many distinct values of standard deviation are actually possible? The answer is 4, but not because SD is restricted to the integers 1 through 4. The answer is 4 because there are 4 distinct types of sets that can arise under the constraints, and each produces a different SD:
- {1, 1, 1, 5} giving SD = \(\sqrt{3}\)
- {1, 1, 3, 5} giving SD = \(\frac{\sqrt{11}}{2}\)
- {1, 1, 5, 5} giving SD = 2
- {1, 3, 3, 5} giving SD = \(\sqrt{2}\)
So the standard deviation can take exactly four different values across all possible sets.
Check complete solution here: https://gmatclub.com/forum/e-is-a-colle ... ml#p769236
Hop it helps.
