Data Sufficiency

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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If you multiply all of the values in a set by some constant k, you will multiply the mean, median, range and standard deviation of that set by k. So here, if we multiply everything in set A by 1/4, we will make the standard deviation 1/4 of its previous value. Since standard deviation is always zero or greater, this will decrease the standard deviation (or leave it unchanged in the one case where the std deviation is 0). So Statement 1 is sufficient, and since Statement 2 clearly is not, the answer is A.