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# Which of the following set has the smallest standard deviation ?

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Math Expert
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Which of the following set has the smallest standard deviation ?  [#permalink]

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30 Jan 2020, 03:01
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Which of the following set has the smallest standard deviation ?

A. {2, 2, 3, 5, 7}
B. {2, 2, 2, 2, 79}
C. {2, 2, 3, 4, 7}
D. {2, 2, 6.9, 4, 3}
E. {8, 2, 2, 3, 5}

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Which of the following set has the smallest standard deviation ?  [#permalink]

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31 Jan 2020, 21:44
Bunuel wrote:
Which of the following set has the smallest standard deviation ?

A. {2, 2, 3, 5, 7}
B. {2, 2, 2, 2, 79}
C. {2, 2, 3, 4, 7}
D. {2, 2, 6.9, 4, 3}
E. {8, 2, 2, 3, 5}

Solution:
We will solve this problem by using the definition of standard deviation.
The best method to solve this problem is to calculate the mean of each set and after that, we will find the difference between mean and entry of the set. The least scattered set will have the least standard deviation.
Option A: $$\{2, 2, 3, 5, 7\}$$
• Mean = $$\frac{19}{5} =3.8$$
• Now, The difference between mean and each element =$$\{-1.8, -1.8, -0.8, 1.2, 3.2\}$$
Option B: $$\{2, 2, 2, 2, 79\}$$
• Mean = $$\frac{87}{5}=17.4$$
• Now,The difference between mean and each element =$$\{-15.4, -15.4, -15.4, 15.4, 61.6\}$$
Option C: $$\{2, 2, 3, 4, 7\}$$
• Mean = $$18/5= 3.6$$
• Now,The difference between mean and each element =$$\{-1.6, -1.6, -0.6, 0.4, 3.4\}$$
Option D:$$\{2, 2, 6.9, 4, 3\}$$
• Mean =$$\frac{ 17.9}{5} = 3.58$$
• Now,The difference between mean and each element =$$\{-1.58, -1.58, 3.32, 0.42, -0.58\}$$
Option E:$$\{8, 2, 2, 3, 5\}$$
• Mean = $$\frac{20}{5}=4$$
• Now,The difference between mean and each element = $$\{4, -2, -2, -1, 1\}$$
We can see that D is the least scattered.
hence, the correct answer is Option D.
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Re: Which of the following set has the smallest standard deviation ?  [#permalink]

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01 Feb 2020, 01:55
Is there a shortcut?

Posted from my mobile device
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Joined: 03 Oct 2016
Posts: 36
Re: Which of the following set has the smallest standard deviation ?  [#permalink]

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03 Feb 2020, 16:22
Bunuel wrote:
Which of the following set has the smallest standard deviation ?

A. {2, 2, 3, 5, 7}
B. {2, 2, 2, 2, 79}
C. {2, 2, 3, 4, 7}
D. {2, 2, 6.9, 4, 3}
E. {8, 2, 2, 3, 5}

karishma Veritasprep, Bunuel..
Pls tell us the best way to solve this question..
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Re: Which of the following set has the smallest standard deviation ?  [#permalink]

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03 Feb 2020, 23:47
the more closely packed the no.s are the least is the standard deviation
only option D has 6.9 and all other options have like 8 and 79 which are very large... so the shortcut is to find the least scattered or closely packed no.s so 'D' is the answer
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Re: Which of the following set has the smallest standard deviation ?  [#permalink]

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04 Feb 2020, 08:02
Here's my non-math solution..

Compare A to E and notice that the only difference is {2, 2, 3, 5, 7} {8, 2, 2, 3, 5} , since 7 is closer to the mean than 8 it will have a smaller standard deviation, eliminate E. Compare A to C and notice the only difference is the 5 vs 4, since 4 is closer to the mean eliminate A. The 79 in B will give it a huge standard deviation so eliminate it. Compare C and D and notice the only difference is 7 vs 6.9, using the same logic as before, 6.9 being closer to the mean, eliminate C. D remains.

ANS) D
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Re: Which of the following set has the smallest standard deviation ?  [#permalink]

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08 Feb 2020, 19:14
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Bunuel wrote:
Which of the following set has the smallest standard deviation ?

A. {2, 2, 3, 5, 7}
B. {2, 2, 2, 2, 79}
C. {2, 2, 3, 4, 7}
D. {2, 2, 6.9, 4, 3}
E. {8, 2, 2, 3, 5}

We must remember that the more spread the data points are away from the mean, the larger the standard deviation. To start, we can rule out answer B, since 79 is quite far from the mean of answer B and thus will cause a large standard deviation. Looking at the remaining answer choices, we should see that each answer choice shares 2, 2, 3. Additionally:

A) has 5 and 7

C) has 4 and 7

D has 4 and 6.9

E) has 5 and 8

The two numbers that are closest to 2 and 3 will give the overall set the smallest standard deviation. Thus, we see that choice D is the correct answer.

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Re: Which of the following set has the smallest standard deviation ?   [#permalink] 08 Feb 2020, 19:14
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