Hey guys,
Standard Deviation is a pretty unique topic on the GMAT - because it's fairly labor-intensive thing to calculate, you won't have to actually calculate it, but you will need to conceptually understand what it means. It's meaning is pretty well-defined by its name - it's the typical amount that the data points deviate from the mean. So, essentially, you're asking yourself in this question "do the data points in set S deviate further from the mean of set S than the data points in set T deviate from their mean?"
Range can play a part in Standard Deviation - the larger the range of the set, the more the highest and lowest values deviate from the mean. But there is certainly a need for both statistical measures. Consider these sets:
Set S (larger range): 1, 5, 5, 5, 6, 6, 6, 11
Set T (smaller range): 1, 2, 2, 2, 9, 9, 9, 10
Here, even though the range of S is slightly larger, its data points are typically right on the average - they tend not to deviate too much, except for those two outliers (1 and 11) that form the range.
Set T, even with a smaller range, tends not to have its data points ever that close to the average - they hug the outer limits, so there's generally a pretty large deviation from the mean of 5.
Therefore, statement 1 is not sufficient - a larger range does not guarantee a larger standard deviation.
Statement 2 is wholly irrelevant - Standard Deviation measures "typical deviation from the mean", whatever that mean is. Consider this - in either set, would making all of the values negative change the standard deviation?
Set A: 1, 5, 5, 5, 6, 6, 6, 11
Set A (but negative) -1, -5, -5, -5, -6, -6, -6, -11
The deviations are the same - in A, the average is 6, and the middle data points (5s and 6s) deviate by either 0 or 1, with the outliers deviating by 5. In the "negative A", the average is -6, and the deviations are the same (-5 deviates by 1, -6 doesn't deviate, and the outliers deviate by 5).
So the actual value of the mean doesn't impact the standard deviation as long as the set itself maintains the same distances from each data point to the mean. Statement 2 doesn't add any value at all, and therefore won't help with Statement 1, either.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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