another stan dev problem

[imadummy]

Set A consists of all prime numbers between 10 and 25; Set B consists of consecutive even integers, and Set C consists of consecutive multiples of 7. If all the three sets have an equal number of terms, which of the following represents the ranking of these sets in an ascending order of the standard deviation?

C,A,B
A,B,C
C,B,A
B,C,A
B,A,C

[VP_RedSoxFan]

We can start by figuring out what each set looks like, as much as possible.

A = {11,13,17,19,23}
B = {5 even numbers}
C = {5 consecutive multiples of 7}

Since we're just comparing the standard deviations relative to each other, no need to whip out the big formula and try to calculate each Set's stdev. Again standard dev measures the average distance of the items in the set from the mean. We can see clearly that the set of even numbers {A} will be most closely clustered while the spread of items in Set C would have the largest standard deviation.

It is worth mentioning that you can lose a hard earned point here if you don't read the question carefully and order them in ascending order as asked. Answer [A] would be a "gotcha" answer choice for the unwarying GMAT test-taker.

Correct answer, according to me: [E]

Hope this helps.

[gmatinjuly]

Ok mY answer is also E

This is how I did it ...

Deviation = sum of deviation from mean

Prime Numbers = 11, 13 , 17 , 19, 23
Even Numbers = x-4, x-2 , x , x+2, x+ 4
Multiples of 7 = y-14, y-7, y , y+ 7 , y+ 14

For EVen numbers max value of further term is 4 from mean
For multiple of 7 it is 14
and for prime numbers its not evenly spread but from 17 it is roughly +/- 6

So even number least spread, then prime and most is multiples of 7

So Even (B). prime (A) and Multiples of 7 (C)

[Stuart@KaplanGMAT]

Deviation = sum of deviation from mean

This is not quite accurate. The SD deviation is a lot more complicated and involves squares and roots.

For the purposes of the GMAT, you will NEVER need to calculate standard deviation. Here's what you may need to know:

(1) the more spread out the terms are, the higher the SD; the more compact the terms are, the lower the SD.

GMAT questions testing this concept will involve easy to evaluate choices, so a quick glance will tell you what set has a higher SD.

(2) in graph form, the steeper the curve, the lower the SD; the flatter the curve, the higher the SD (i.e. a very steep bell means that the numbers are tightly packed and the SD will be lower than a flat bell in which the numbers are more spread out).

(3) to calculate the SD of a set, one needs to know the number of terms and the exact spacing of the terms. (3) arises most often in the context of a data sufficiency question. Of course, if we know all the terms in a set, we can calculate SD, but we don't actually need to know what the terms are.

For example, if we know that set S is made up of 5 consecutive multiples of 7, we can calculate SD even though the set could be {7, 14, 21, 28, 35} or {21, 28, 35, 42, 49} (or lots and lots of other things).

(4) You may be told the value of 1 SD and asked which numbers in a set fall inside (or outside) of a certain range.

[imadummy]

Thanks, guys. The stats stuff really throws me off.