GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 01 Apr 2020, 01:18

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 62396
Which of the following set has the smallest standard deviation ?  [#permalink]

### Show Tags

30 Jan 2020, 03:01
00:00

Difficulty:

25% (medium)

Question Stats:

65% (01:01) correct 35% (01:14) wrong based on 60 sessions

### HideShow timer Statistics

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}

_________________
GMATWhiz Representative
Joined: 07 May 2019
Posts: 407
Location: India
Which of the following set has the smallest standard deviation ?  [#permalink]

### Show Tags

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.
_________________

GMAT Prep truly Personalized using Technology

Prepare from an application driven course that serves real-time improvement modules along with a well-defined adaptive study plan. Start a free trial to experience it yourself and get access to 25 videos and 300 GMAT styled questions.

Score Improvement Strategy: How to score Q50+ on GMAT | 5 steps to Improve your Verbal score
Study Plan Articles: 3 mistakes to avoid while preparing | How to create a study plan? | The Right Order of Learning | Importance of Error Log
Helpful Quant Strategies: Filling Spaces Method | Avoid Double Counting in P&C | The Art of Not Assuming anything in DS | Number Line Method
Key Verbal Techniques: Plan-Goal Framework in CR | Quantifiers the tiny Game-changers | Countable vs Uncountable Nouns | Tackling Confusing Words in Main Point
Intern
Joined: 19 Jan 2020
Posts: 5
Re: Which of the following set has the smallest standard deviation ?  [#permalink]

### Show Tags

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

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

### Show Tags

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..
Intern
Joined: 22 May 2019
Posts: 7
Re: Which of the following set has the smallest standard deviation ?  [#permalink]

### Show Tags

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
Intern
Joined: 24 Jan 2020
Posts: 9
Location: United States (TX)
Schools: McCombs
Re: Which of the following set has the smallest standard deviation ?  [#permalink]

### Show Tags

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
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9906
Location: United States (CA)
Re: Which of the following set has the smallest standard deviation ?  [#permalink]

### Show Tags

08 Feb 2020, 19:14
1
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.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
197 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: Which of the following set has the smallest standard deviation ?   [#permalink] 08 Feb 2020, 19:14
Display posts from previous: Sort by