Standard Deviation

[rishab1988]

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.

[Night reader]

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.