statistics

[shrutee]

If sets A and B have the same number of items,is the standard deveiation of set A greater than the standard deviation of set B?

(1)The range of set A is greater than that range of set B

(2)Set A and Set B are both evenly spaced

[Geva@EconomistGMAT]

If sets A and B have the same number of items,is the standard deveiation of set A greater than the standard deviation of set B?

(1)The range of set A is greater than that range of set B

(2)Set A and Set B are both evenly spaced

This is not a real GMAT question. The term "evenly spaced" is vague and not well defined - it is not clear whether the terms are evenly spaced (i.e. have even spaces between them = consecutive integers, or consecutive even integers), or the sets are evenly spaced (i.e. the terms are evenly spaced across the respective range of the set.

The SD is a measure of the set's dispersal around its average. The average itself is not important - the deviations of the terms FROM that average is. Thus, if two sets have different averages, but the same dispersal pattern of terms AROUND that average, then these sets will have the same Standard deviation.

For example the two sets 3,4,5 and 1007, 1008, 1009 have the same standard deviation, simply because they have the same dispersal patterns: the average is the middle number, and there is one term deviating "1 above" the average, and 1 term deviating "1 below" the average.

Back to our DS question: when asking "is the SD of A greater than the SD of B?", the question is really asking whether the terms in A have a "wider" dispersal pattern around their average than the terms of B.

Stat. (1) tells you something about the highest and lowest terms in A and B, but doesn't tell you what happens in between. It is indeed possible that A's terms are more dispersed than Bs based on the the fact that A's terms "stretch" over a greater distance, but it is also possible that A's smallest and greatest terms are outliers, and the rest of A's terms are huddled around the average, making for a smaller standard deviation. We simply don't know whether A has a greater SD or not, so stat. (1) is insufficient.

Stat. (2) This one really depends on what "evenly spaced" means.

If it means that the terms in the sets are consecutive integers, then the sets will have the same number of consecutive terms, and as the explanation above shows, this means that they will have an equal SD regardless of the average.
for example, the twin sets
A {3,4,5}T
B {9,10,11}
Could be considered "evenly spaced" - they have the same spacing between terms.

The answer to the question stem would be "no", as the SD of A is NOT greater than the SD of B, but that is still sufficient. The answer would be B.

If, however, it merely means that the terms are evenly spaced across the range of each set, then you also need to know that range. For example, consider the following two sets

A: {3, 5, 7}
B: {3, 4 ,5}

These two sets could be considered "evenly spaced" - their terms are spaced evenly across their respective range.

In this case, you need stat. (1) as well. If the same number of terms are "stretched" in an even spacing across a greater range in A, then A will have a greater SD than B. The answer in this case will be C.

[navami]

Thanks Geva

[verbalfight]

Great explanation!

[GMATGuruNY]

I posted a explanation here:

https://www.beatthegmat.com/standard-dev ... 73739.html