Question from MGMAT CAT Test

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Question from MGMAT CAT Test

by Oneva » Mon Jan 24, 2011 5:48 pm
If the standard deviation of Set Y is 4, what are the greatest and least values that are within one standard deviation of the mean?

(1) The median of Set Y is 5.

(2) The mean of Set Y is 6.

OA isB

Would someone please be able to explain why? i don't have a very comfortable understanding of standard deviations.

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by Night reader » Mon Jan 24, 2011 6:56 pm
Oneva wrote:If the standard deviation of Set Y is 4, what are the greatest and least values that are within one standard deviation of the mean?

(1) The median of Set Y is 5.

(2) The mean of Set Y is 6.

OA isB

Would someone please be able to explain why? i don't have a very comfortable understanding of standard deviations.
standard deviation, S is a measure of central tendency, along with the mean, median and mode. S^2 is calculated as Sigma (sum) of all distribution values subtracted from mean and squared. S^2 is called a Variance and explains how the distributed values are dispersed on the number line, along the distribution chart or in the space. Variance is the standard deviation just in the power of 2, and it describes the variability. Hence S is Sqrt(Variance) - the purpose or use of S or standard deviation is the same, except its tendency measure is more centered i.e. focused on the mean of values... google standard deviation and you will find more academic explanation of this concept on the internet.

Here st(2) offers mean as the parameter to satisfy our central tendency measurement, hence it's Sufficient.

why we need S and Variance - GMAT of course now... in Business School you should use these stats parameters to evaluate the risk factors in the distributed raw of data. Thus, Variance/Mean=Coefficient of Variance or CV - decimal interpretation of the risk present in the data not matching with our required central tendency parameters. Later you should use the hypothesis theory for proving H1 or H0 of the certain stats parameters to be valid or not, mean as well as S and Variance are only the very basic things you would have to apply ... there are also f, chie square, t and z-stats :)

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by Rahul@gurome » Mon Jan 24, 2011 9:57 pm
Oneva wrote:... i don't have a very comfortable understanding of standard deviations.
For a data set, standard deviation is the measure of dispersion or variation of the data from the mean or average. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.

It is defined as the the square root of the average of the squared differences from the Mean. Yes, the definition seems a bit confusing. For a explained definition with an example, visit this link : https://www.mathsisfun.com/data/standard-deviation.html

But for this particular question, we don't need to use those concepts.
Oneva wrote:If the standard deviation of Set Y is 4, what are the greatest and least values that are within one standard deviation of the mean?

(1) The median of Set Y is 5
(2) The mean of Set Y is 6
If we just omit the term "standard deviation" from the question, then the question is asking What are the greatest and least values that are within a distance of 4 from the mean?

Hence, if we know the mean, we can easily determine those values as greatest = (Mean + 4) and least = (Mean - 4)

Now, statement 1 is NOT sufficient as it doesn't provide the mean. Buts statement 2 is SUFFICIENT.

The correct answer is B.
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by towerSpider » Tue Jan 25, 2011 7:42 am
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