BTGmoderatorDC wrote:Is the standard deviation of Set A greater than or equal to the standard deviation of Set B?
(1) Set B can be formed by dividing each value in Set A by 4.
(2) Set A consists of 7 unique numbers.
OA A
Source: Veritas Prep
The standard deviation measures the spread of the data w.r.t. its mean value. It is applied in comparing sets of data which may have the same mean but a different range. For example, the mean of the following two is the same: 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30. However, the second is clearly more spread out. If a set has a low standard deviation, the values are not spread out too much.
We have to determine whether
SD of set A ≥ SD of set B
Let's take each statement one by one.
(1) Set B can be formed by dividing each value in Set A by 4.
Case 1:
Say, Set A: {4, 4, 4}; thus, its SD = 0 since there is no deviation of numbers w.r.t. their mean (= 4).
Thus, Set B: {1, 1, 1}; thus, its SD = 0 since there is no deviation of numbers w.r.t. their mean (= 1).
=> SD of set A = SD of set B. The answer is Yes.
Case 2:
Say, Set A: {0, 4, 8,}; thus, its SD = some value (> 0), say x. Note that SD is always a non-negative number.
Thus, Set B: {0, 1, 2}; thus, its SD = some value (> 0), say y.
Note that x > y. Since after dividing each number of Set A by 4, the spread of numbers in Set B is less, its SD would be less than that of Set A.
=> SD of set A > SD of set B. The answer is Yes.
Sufficient.
(2) Set A consists of 7 unique numbers.
We have no information about Set B. Insufficient.
The correct answer:
A
Hope this helps!
-Jay
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