Which of the following correctly lists the data sets in order of least

Question

Tough and Tricky questions: Statistics and Sets Problems

Which of the following correctly lists the data sets in order of least to greatest standard deviation?

I. 2, 13, 55, 12, 14, 64 
II. 32, 32, 32, 32, 32, 32 
III. 37, 38, 39, 40, 41, 42

A. I, II, III
B. I, III, II
C. II, I, III
D. II, III, I
E. III, II, I

Kudos for a correct  solution .

anupamadw · Answer

out of three given sets,
II has all numbers same, so it has zero standard deviation hence it is Least 
only answer choices C and D have II in least position.

Out of I ans III
III has consecutive numbers , hence all are closedly spaced hence std deviation will be less
while in I,numbers are spread widely hence std deviation should be more than III

hence order should be II, III,I
IMO D

can someone please validate if this is correct?

Bunuel · Answer

OFFICIAL SOLUTION:

(D) To answer a question such as this, you DO NOT need to know how to calculate standard deviation. You simply need to understand how to compare standard deviations of different sets. The more spread out the numbers are, the greater the standard deviation will be. Even one or two numbers that are much larger or smaller than the others will cause the standard deviation to rise drastically.

Here, there is a very small variation in the terms of set II, so it has the smallest standard deviation. Set III has some variation, but the terms are very close to each other, so it has the next larger standard deviation. Finally, set I has two terms (18 and 64) that are far from the other four terms. Therefore, set I has the largest standard deviation. So the correct order from least to greatest standard deviation is II, III, I.

The correct answer is choice (D).

veergmat · Answer

STANDARD DEVIATION: It is a variation from the mean value or when plotted on graph it shows dispersion from the mean. So lets see the problem: I. 2,12,13,14,55,64..................... data are dispersed in wide range from 2 to 64. II. No deviation as mean is 32 only. III. Dispersed data but in very low range 37 to 42 as compared to 'I' Answer is clearly II, III,I. Why to take pain of solving it ?? :wink:

buddyisraelgmat · Answer

Hi Bunuel

I just took the 1st test from 800 score and the official question is as follows

Which of the following correctly lists the data sets in order of least to greatest standard deviation?

I. 18, 25, 25 , 25, 26, 64 
II. 32, 32, 32,  30 , 32, 32 
III. 37, 38, 39, 40, 41, 42

I know I has the greatest SD but  I am unable to figure out how to compare II & III - Which has a greater SD ?

Pls explain

Thanks

Alchemist14 · Answer

Hi buddyisraelgmat,

Arranging II: 30,32,32,32,32,32.  Mean is close to 32 - All elements except 30 are 32.
Set III: 37, 38, 39, 40, 41, 42.  Mean is 39.5

You can see that the elements in Set III are more widespread from the mean than are the elements in Set II.

Thus SD(III)>SD(II)

Alchemist14

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Which of the following correctly lists the data sets in order of least

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Which of the following correctly lists the data sets in order of least

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards