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Standard Deviation of Even numbers

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Standard Deviation of Even numbers

by suchoudh » Sun Jan 24, 2010 3:42 pm
Series P consists of 5 items. The standard deviation of the items in series P is S. Is S>2?

(1) All the items in series P are different even numbers between 1 and 19.

(2) The smallest number in the series is 10.


(A) statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
(B) statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
(C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked;
(D) EACH statement ALONE is sufficient to answer the question asked;
(E) statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

OA C
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by Stuart@KaplanGMAT » Sun Jan 24, 2010 7:25 pm
suchoudh wrote:Series P consists of 5 items. The standard deviation of the items in series P is S. Is S>2?

(1) All the items in series P are different even numbers between 1 and 19.

(2) The smallest number in the series is 10.


(A) statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
(B) statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
(C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked;
(D) EACH statement ALONE is sufficient to answer the question asked;
(E) statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

OA C
While you never have to calculate SD on the GMAT, you may be tested on the general concept, e.g. knowing what's required to calculate SD. I'm a bit surprised by this question, since it does require more knowledge of SD (we have to determine if it's greater than 2, rather than just determine what it is) - what's the source of the question? The answer also seems to be wrong.

To calculate, we need to know 2 facts about the set:

1) the number of terms; and
2) the exact spacing of the terms.

Of course, if we know all the numbers, we can calculate SD; however, we don't need the actual terms.

Looking at this question:

From the stem, we know that we have 5 terms. So, if we know the spacing, we can calculate SD.

1) set could be {2,4,6,8,10} or {2,4,6,16,18}, which have different spacing. The second set definitely has a SD > 2, so we can get a "yes" answer. If you do the math, the first set also has a SD of more than 2 (3.16228 to be exact), so this statement actually gives us a definite "yes" answer to the question: sufficient.


2) Set could be {10, 11, 11, 11, 11} for a "no" answer or {10, 100, 1000, 10000, 1000000} for a "yes" answer: insufficient.

So, the answer should be A, not C.

If the question had asked for the SD instead of "is the SD > 2", then we'd need both statements, since together we can determine the exact set.
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by ajith » Mon Jan 25, 2010 1:15 am
Stuart Kovinsky wrote: From the stem, we know that we have 5 terms. So, if we know the spacing, we can calculate SD.

1) set could be {2,4,6,8,10} or {2,4,6,16,18}, which have different spacing. The second set definitely has a SD > 2, so we can get a "yes" answer. If you do the math, the first set also has a SD of more than 2 (3.16228 to be exact), so this statement actually gives us a definite "yes" answer to the question: sufficient.
Just to elaborate how to find SD

Consider the set - 2,4,6,8,10

You find the mean of these - (2+4+6+8+10)/5 =6

Now find the difference between mean and each term and square and sum = (2-6)^2+ (4-6) ^2 + (6-6)^2 + (8-6)^2+(10-6) ^2 = 40

now divide this by number of terms -1 = 40/(5-1) = 10

Take the square root of the number you got in the previous step is the standard deviation = Sqrt(10) = 3.16227766
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by Stuart@KaplanGMAT » Mon Jan 25, 2010 11:57 am
ajith wrote: Just to elaborate how to find SD

Consider the set - 2,4,6,8,10

You find the mean of these - (2+4+6+8+10)/5 =6

Now find the difference between mean and each term and square and sum = (2-6)^2+ (4-6) ^2 + (6-6)^2 + (8-6)^2+(10-6) ^2 = 40

now divide this by number of terms -1 = 40/(5-1) = 10

Take the square root of the number you got in the previous step is the standard deviation = Sqrt(10) = 3.16227766
Also just to elaborate: you do NOT need to know this formula for the GMAT!

In real life if you need to calculate standard deviation you go to Google, type in "standard deviation calculator", click on the link and plug in your numbers (or you use a calculator, Excel or accounting department); on the GMAT we're never expected to do tedious and complicated calculations.
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by ajith » Mon Jan 25, 2010 12:01 pm
Stuart Kovinsky wrote: Also just to elaborate: you do NOT need to know this formula for the GMAT!

In real life if you need to calculate standard deviation you go to Google, type in "standard deviation calculator", click on the link and plug in your numbers (or you use a calculator, Excel or accounting department); on the GMAT we're never expected to do tedious and complicated calculations.
Please ignore my previous post as GMAT does not want you to know that (probably it is a secret!!!)

We won't study anything GMAT does not want us to :)
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by Stuart@KaplanGMAT » Mon Jan 25, 2010 12:53 pm
ajith wrote:
Stuart Kovinsky wrote: Also just to elaborate: you do NOT need to know this formula for the GMAT!

In real life if you need to calculate standard deviation you go to Google, type in "standard deviation calculator", click on the link and plug in your numbers (or you use a calculator, Excel or accounting department); on the GMAT we're never expected to do tedious and complicated calculations.
Please ignore my previous post as GMAT does not want you to know that (probably it is a secret!!!)

We won't study anything GMAT does not want us to :)
Well, if you're studying for the GMAT, then you don't want to clutter your mind with unnecessary (and very complicated) formulae.

If you're studying for a stats exam (on which you're allowed to use a calculator), or just have a burning desire to understand standard deviation (chicks dig it!), then memorize away!
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by suchoudh » Mon Jan 25, 2010 4:25 pm
Thanks for the detailed explanation Stuart! The answer is indeed 1(A).

Sorry, the question belongs to a test prep company, whose name I cannot disclose.
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by ajith » Mon Jan 25, 2010 8:12 pm
Stuart Kovinsky wrote:[
Well, if you're studying for the GMAT, then you don't want to clutter your mind with unnecessary (and very complicated) formulae.
And, they say we make use of only 5% of the brain's capacity!
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by gmat.kiddo » Tue Jan 26, 2010 1:55 pm
Why is the denominator "N-1", shouldn't this be "N" since the sample size is small? Well the answer still would not change, but i am just brushing up my basic stat. :)
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by ajith » Tue Jan 26, 2010 8:49 pm
gmat.kiddo wrote:Why is the denominator "N-1", shouldn't this be "N" since the sample size is small? Well the answer still would not change, but i am just brushing up my basic stat. :)
The rule is one should use n-1 if it is a sample and n if it is the population

If we are estimating the population SD from a sample, we use n-1. If we are estimating population SD using all the numbers in the population then we use n. But, here no such indication is there
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