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Which data set has the greater standard deviation, data set

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Which data set has the greater standard deviation, data set

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Which data set has the greater standard deviation, data set K or data set L?

(1) Every element in data set K is a multiple of 3.

(2) Every element in data set L is a multiple of 9.

OA E

Source: Magoosh

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BTGmoderatorDC wrote:
Which data set has the greater standard deviation, dataset K or dataset L?

(1) Every element in dataset K is a multiple of 3.

(2) Every element in dataset L is a multiple of 9.

OA E

Source: Magoosh
Certainly, each statement is not sufficient since each statement gives information about only one dataset.

Combining the two statements, we get

Case 1: Say dataset K: {3, 3} and dataset L: {9, 18}

Standard deviation of dataset K = 0 since each element is the same; however, standard deviation of dataset L > 0 since each element is NOT same. The answer is dataset L.

Case 2: Say dataset K: {3, 6} and dataset L: {9, 9}

Standard deviation of dataset L = 0 since each element is the same; however, standard deviation of dataset K > 0 since each element is NOT same. The answer is dataset K.

No unique answer. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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BTGmoderatorDC wrote:
Which data set has the greater standard deviation, data set K or data set L?

(1) Every element in data set K is a multiple of 3.

(2) Every element in data set L is a multiple of 9.

Source: Magoosh
\[?\,\,:\,\,\,{\sigma _{\max }}\,\,\left( {K\,\,{\text{or}}\,\,L} \right)\]
\[\left( {1 + 2} \right)\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,{\text{K}} = \left\{ {0,0} \right\}\,\,\,;\,\,\,L = \left\{ {0,9} \right\}\,\,\,\, \Rightarrow \,\,\,\,? = L \hfill \\
\,{\text{Take}}\,\,{\text{K}} = \left\{ {0,3} \right\}\,\,\,;\,\,\,L = \left\{ {0,0} \right\}\,\,\,\, \Rightarrow \,\,\,\,? = K \hfill \\
\end{gathered} \right.\]

The correct answer is therefore (E).


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

POST-MORTEM: in this very special situation, a careful reader may correctly mention that K=L={0} is enough to guarantee the correct answer is (E).
(We don´t want to explain this delicate issue here. We have just mentioned it because our own students will correctly think about that option at once!)

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Course release PROMO : finish our test drive till 30/Nov with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!

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BTGmoderatorDC wrote:
Which data set has the greater standard deviation, data set K or data set L?

(1) Every element in data set K is a multiple of 3.

(2) Every element in data set L is a multiple of 9.
Every element in data set K is a multiple of 3.

Since we don’t know anything about set L, statement one alone is not sufficient.

Statement Two Alone:

Every element in data set L is a multiple of 9.

Since we don’t know anything about set K, statement two alone is not sufficient.

Statements One and Two Together:

Even with both statements, it’s still not sufficient to answer the question. For example, if set K is {3, 6} and set L is {9, 18}, then set L has a larger standard deviation (recall that numbers are further apart from one another produce a larger standard deviation). However, if set K is {3, 3} and set L is {9, 9}, then the standard deviation of set K and set L is equal, and it’s 0 (recall that a set with all numbers the same has standard deviation of 0).

Answer: E

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