Question
A particular data set has a standard deviation of x, with an average (arithmetic mean) of 0.3. If x is positive, which of the following sets of numbers, when added to the set, must create a new standard deviation that is less than x?
1.3 and 1.3
0.7 and 0.3
1.3 and 0.3
0.3 and 0.3
0 and 1.3
Scott Woodbury-Stewart
Founder and Expert GRE Instructor
Text Solution:
We should keep in mind that the closer the data points are to the mean, the smaller the standard deviation. If we add only one 0.3 to the data set and add one other number, we cannot be sure that the new standard deviation is less than the old one. Depending on how close the numbers in the data set are to the mean, the other number we add to the set may increase the standard deviation. On the other hand, if we add two additional values of 0.3 to the data set, the standard deviation will definitely decrease. Thus, the new standard deviation will be less than x, the original standard deviation. Remember that when a set has a positive standard deviation, adding numbers to the set that are equal to the mean will decrease the standard deviation.
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