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standard deviation of the integers in list X equal to zero

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by fiza gupta » Sun Nov 06, 2016 11:45 am
1) Range = 3
Range = highest number - smallest number
to make S.D = 0 all numbers should be same or Range = 0
Range = 3 implies that all numbers are not same so S.D will not be 0
SUFFICIENT

2) average = 5
its not mentioned that all numbers are same or different
if all 8 numbers are 5/same then S.D = 0 but if all are different then S.D is not 0
INSUFFICIENT

SO A
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by [email protected] » Sun Nov 06, 2016 12:27 pm
Hi Needgmat,

Standard Deviation is a relatively rare concept on the GMAT (you'll likely see it just once on Test Day) and you'll never be asked to actually calculate SD. Thus, you really just need to know the general concepts behind the subject. In this prompt, the 'key' is understanding what a 0 SD means... That can only happen when ALL of the values are the SAME.

We're told that list X contains 8 integers (as an aside, the fact that they're integers or that there are 8 of them is actually irrelevant). We're asked if the SD of the numbers is 0. This is a YES/NO question.

(1) The range of the integers in list X is 3.

Since the range = 3, then we know that at least one of the integers is different from the others. Thus, the SD CANNOT be 0 and the answer to the question is ALWAYS NO.
Fact 1 is SUFFICIENT

(2) The average (arithmetic mean) of the integers in list X is 5.

IF... ALL the integers are 5, then the SD is 0 and the answer to the question is YES.
IF... Four of the integers are 4 and four of the integers are 6, then the SD is NOT 0 and the answer to the question is NO.
Fact 2 is INSUFFICIENT

Final Answer: A

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by Jay@ManhattanReview » Wed Feb 01, 2017 9:37 pm
Needgmat wrote:List X contains 8 integers. Is the standard deviation of the integers in list X equal to zero?

(1) The range of the integers in list X is 3.

(2) The average (arithmetic mean) of the integers in list X is 5.

OAA
In much simpler terms, Standard Deviation (SD) is a measure of deviations of all the terms of a set w.r.t. their arithmetic mean. SD measures how far the terms are spread w.r.t. mean. Closer the terms are to their mean, less is the SD and vice versa.

Say, in three matches, Messi scored 1, 0, and 8 goals, thus his mean score = 3 goals per match. His Range = 8 - 0 = 8.

Now, say, in three matches, Ronaldo scored 2, 2, and 2 goals, thus his mean score = 2 goals per match. His Range = 2 - 2 = 0.

We see that Ronaldo is more consistent than Messi. His goals in the number of goals each match has NOT deviated from the mean. Thus, SD for Ronaldo = 0. Whereas, we see that for Messi, there is a deviation for each of three matches. His SD must not be equal to 0. Since the computation of SD is beyond the scope of the GMAT, I will not compute it. Hope the concept is clear to you.

Coming to the original question...

S1: The range of the integers in list X is 3.

This is a case of Messi. Since the range is not equal to 0, there must be some deviation. sufficient.

S2: The average (arithmetic mean) of the integers in list X is 5.

In the case of Messi, the mean is 3, and in the case of Ronaldo, the mean is 2, but they do not tell anything about their ranges. Messi can make his mean of 3 by scoring 3, 3, and 3 goals in each match, making SD = 0. Or, he can score 1, 0, and 8 goals, making SD > 0. Inconclusive.

By the same reasoning, S2 is insufficient.

The correct answer: A

Hope this helps!

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by ceilidh.erickson » Sat Feb 04, 2017 11:24 am
Knowing an AVERAGE will never help you to answer a STANDARD DEVIATION question, and vice versa. A RANGE will only help you to determine whether the SD is 0 (if the range = 0, the SD = 0).

Very generally speaking, knowing one statistic will rarely help you to answer a question about another. Here is a breakdown:

If the question is asking about:

1) MEAN
- helpful: sum, number of terms
- not helpful: median (unless it's an evenly spaced set), range (or smallest or largest value), standard deviation

2) MEDIAN
- helpful: number of terms
- maybe helpful: whether it's an odd or even number of terms
- not helpful: mean (unless evenly spaced), range (or smallest or largest value), standard deviation

3) STANDARD DEVIATION
- helpful: knowing the value of every term
- maybe helpful: range (if 0)
- not helpful: anything else

4) RANGE
- helpful: smallest and largest values
- maybe helpful: standard deviation (if 0)
- not helpful: anything else (unless evenly spaced and you know the # of terms)

5) SUM
- helpful: average and number of terms
- maybe helpful: starting or ending value (if you have # of terms)
- not helpful: median (unless evenly spaced and you know # of terms), range, standard deviation

Hope this helps!
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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