Standard Deviation

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rishab1988: Master | Next Rank: 500 Posts; Posts: 332; Joined: Tue Feb 09, 2010 3:50 pmFollowed by: 7 members; Thanked: 41 times; GMAT Score:720

by rishab1988 » Tue Nov 23, 2010 11:34 am

For a certain exam, was the standard deviation of the scores for students U, V, W, X, Y and Z less than the standard deviation of the scores for students A, B and C?

(1) The standard deviation of the scores of students U, V, and W was less than the standard deviation of the scores of students A, B and C on the exam.

(2) The standard deviation of the scores of students X, Y and Z was less than the standard deviation of the scores of students A, B and C on the exam.

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Source: Beat The GMAT — Data Sufficiency | Tue Nov 23, 2010 11:34 am

Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Tue Nov 23, 2010 11:52 am

rishab1988 wrote:For a certain exam, was the standard deviation of the scores for students U, V, W, X, Y and Z less than the standard deviation of the scores for students A, B and C?

(1) The standard deviation of the scores of students U, V, and W was less than the standard deviation of the scores of students A, B and C on the exam.

(2) The standard deviation of the scores of students X, Y and Z was less than the standard deviation of the scores of students A, B and C on the exam.

Standard deviation, S is describing the spread of data (stats)

Statement (1) suggests that U-V-W are clustered close to each other, therefore their S is less than S of A-B-C. However, we are interested in the range of values U-V-W--X-Y-Z, and we don't know what is dispersion among X-Y-Z and what are their values. Not sufficient.

Statement (2) suggests basically the same but for S of X-Y-Z with relation to S of A-B-C. We need to know dispersion among all values U-V-W (?). Insufficient

Together statements (1) and (2) provide separate standard deviations and separate means for two sets. What if we have outliers grouped close to each other and decreasing their own set standard deviations. We do not know for sure how close are these two sets in Statements (1) and (2). We miss information.

Answer E.

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