Bunuel wrote:

Set A: {1, 3, 5, 7, 9}

Set B: {102, 103, 104, 105, 106}

Set C: {-15, -12, -9, -6, -3}

Which of the following properly ranks the sets in terms of their standard deviation, from greatest to least?

A. B, A, C

B. B, C, A

C. A, C, B

D. C, B, A

E. C, A, B

We'll show two approaches.

The first is Logical, and is based on an intuitive understanding of the term 'standard deviation'.

The standard deviation measures the 'spread', that is 'how far apart' the terms in a sequence are from each other.

Since the elements in C are at a distance of 3 from each other, those in B at a distance of 1 and in A at a distance of 2, our order is C >A > B.

(E) is our answer.

The second approach is a (very long) equation-driven, Precise methodology.

As you can see, Logical methods are much faster...

We'll first calculate the mean of each set:

A --> 5, B--> 104, C--> -9

Next we'll calculate the differences from the mean in each set:

A --> {-4, -2, 0, 2, 4} B --> {-2, -1, 0, 1, 2} C--> {-6, -3, 0 3, 6}

Next we'll calculate the square of the differences:

A --> {16, 4, 0, 4, 16} B --> {4, 1, 0, 1, 4} C--> {36, 9, 0, 9, 36}

Next we'll calculate the average of the squares of the differences

A--> 40/5=8 B-->10/5=2 C--> 90/5=16

Finally we'll calculate the square root of the above

A--> 2*sqrt(2) B--> sqrt(2) C--> 4

So, after all that work, we get to C > A > B, same as the above.

(E) is our answer.

_________________

David

Senior tutor at examPAL

Signup for a free GMAT course

We won some awards:

Save up to $250 on examPAL packages (special for GMAT Club members)