Koala wrote:If sets A and B have the same number of terms, is the standard deviation of set A greater than the standard deviation of set B?
1) The range of set A is greater than the range of set B
2) Sets A and B are both evenly spaced sets
From Veritas Prep Free Test ==> OA is C
Standard deviation describes how much the values in a set deviate from the mean. A larger standard deviation indicates that the values are deviating more -- getting farther away from -- the mean. So the question can be rephrased:
Do the values in set A deviate more from the mean than the do values in set B?
Statement 1:
The distance between the biggest value and the smallest value in set A is greater than the distance between the biggest value and the smallest value in set B. But we don't know how all the other values in each set are deviating from the mean, so there is no way to determine the standard deviation. Insufficient.
Statement 2:
When values are evenly spaced, mean = median. Thus the median in each set -- the middle value -- is also the mean. But we can't determine the standard deviation without knowing the distance between each successive pair of terms.
A could be {1,2,3}, and B could be {1,2,3}. The standard deviations are equal.
A could be {100, 200, 300}, and B could be {1,2,3}. The standard deviation of set A is larger.
Insufficient.
Statements 1 and 2:
The values in each set are evenly spaced, so the mean in each set is the median (the middle value). If sets A and B had the same range, their standard deviations would be equal: the biggest value and the smallest value in each set would be the same distance from the mean. But since the range of set A is greater than the range of set B, the biggest value and the smallest value in set A are each further from the median than are the biggest value and the smallest value in set B. Thus, set A has a greater standard deviation. Sufficient.
The correct answer is
C.
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