Which of the following data sets has the third largest standard deviat

Question

Which of the following data sets has the third largest standard deviation?

(A) {1, 2, 3, 4, 5} 
(B) {2, 3, 3, 3, 4} 
(C) {2, 2, 2, 4, 5} 
(D) {0, 2, 3, 4, 6} 
(E) {-1, 1, 3, 5, 7}

chetan2u · Accepted Answer

Hi,

since we are asked to compare 'standard deviation', we should look out for similarity between all the sets..

The SIMILARITY is - the SUM of all sets is equal =15..
and hence average = 15/5 = 3...

Now we have 5 different sets which have AVG as 3, so we will look for the spread of the other elements of set around the AVERAGE..
clearly E has a range of 7-(-1) or 8, and has the highest standard deviation..
Next is D, which has a range of 6-0 or 6..
and THIRD is A

ans A

KarishmaB · Answer

In simple terms, standard deviation is the measure of the spread of the numbers around the mean. More the spread, higher the SD. 
Just imagine how the numbers will be spread around the mean on the number line.

(A) {1, 2, 3, 4, 5} 
Mean is 3.

____1__2__3__4__5_____

(B) {2, 3, 3, 3, 4} 
Mean is 3.

______2__333__4_______

Tighter packed than A
B < A

(C) {2, 2, 2, 4, 5} 
Mean is 3.

______222__3__4__5_____
Not as tight as B but tighter than A
B < C < A

(D) {0, 2, 3, 4, 6} 
Mean is 3.

____0____2__3__4____6_____
More distant than A
B < C < A < D

(E) {-1, 1, 3, 5, 7}
Mean is 3.

____-1____1____3____5____7_____
More distant than D
B < C < A < D < E

So (A) has the third largest SD.

anoopm · Answer

I'm not sure if this approach is right but it would be great if some of the experts can throw some light here...

Size of the range(max element - min element) for each set

A : 5 -1 = 4
B : 4 - 2 =2
C: 5-2 = 3
D:6-0 = 6
E:7- -1 = 8

Number of elements is same for each set.
Based on the range size third largest SD would be set A

Is this approach right?

namnamnam123 · Answer

All choices have the same mean: 3
Standard deviation:
A. 5 -3 or 3 -1 =2 Third highest
B. 4 - 3 or 3 - 2 = 1
C. 5 - 3 =2 or 3 - 2 = 1 so SD (1 and 2)
D. 6-3 or 3-0 =3 Second highest
E. 7-3 or 3 - (-1) =4 Highest

Hence, A is correct!

Kudos if it helps please!

EMPOWERgmatRichC · Answer

Hi All,

Standard Deviation is a relatively rare concept on Test Day (you'll likely see it just once), so it's not a big 'point-gainer' or 'point-loser.' The GMAT will never ask you to actually calculate a Standard Deviation either; you will be tested on your general understanding of the concept though.

In real basic terms, SD is about how 'spread out' a group of numbers is: the more spread out the numbers are, the higher the SD. The closer the numbers are together, the smaller the SD.

In this prompt, we can use the answer choices to 'visually compare' how close the numbers are to one another in each set of numbers.

In Answer A, we have numbers that are evenly spaced out. Compare that set with the set in Answer B:

Answer A: {1,2,3,4,5} 
Answer B: {2,3,3,3,4}

Notice how Answer B's numbers are 'closer together' (the 1 and the 5 in Answer A are replaced by a 2 and a 4 in Answer B).

Now, compare Answer C with Answer A: which group of numbers is 'closer together'? You should notice that the numbers in Answer C are ALSO 'closer together' than the numbers in Answer A. Now we have two answers that have a SMALLER SD than Answer A.

In that same way, how would you describe the 'spread' in Answers D and E, relative to the spread in Answer A. Can you define how they both have a GREATER spread? What would that mean about their SDs, relative to Answer A?

In the end, just by using the concept behind SD, we've found two answers that have greater SDs and two answers that have smaller SDs (relative to Answer A), thus Answer A is the third largest SD of the group.

Final Answer:  A

GMAT assassins aren't born, they're made, 
Rich

DarkHorse2019 · Answer

All the above methods of solving are legit but I approached the problem in the following manner (it took me less than 50 seconds to attempt this):

SD shows how much variation there is from the mean in a given set, in the problem here we need to find the set with the 3rd highest SD - meaning the set were the data points are the 3rd most widespread is the answer.

I have just calculated gaps or differences between consecutive elements of each set.

A) 1,1,1,1 (3rd highest SD)
B) 1,0,0,1
C) 0,0,2,1
D) 2,1,1,2 (2nd highest SD)
E) 2,2,2,2 (1st highest SD)

Hence the answer choice A is correct.

Appreciate your kudos if this helps

jamalabdullah100 · Answer

If you want to do this purely via calculations (even if it takes longer) what is the correct method? I know you work out the mean which is 3 for each of these but then what? Some on this thread have calculated the range to determine which is the answer but is that the correct method?

I tried calculating each element's (in each set) difference from the mean then sum the total of this for each set, but this gives me total differences from mean of 6, 2, 6, 8 and 12 (for A, B, C, D and E respectively) which doesn't help obtain the answer?

kajaldaryani46 · Answer

——-
Wanted to understand the logic behind this approach

Posted from my mobile device

altairahmad · Answer

Does this range method work only when the average of the different sets is same and have same number of elements ?

Sabby · Answer

(A) {1, 2, 3, 4, 5}
= 2 1 1 2 =  6/4

(B) {2, 3, 3, 3, 4}
= 1 0 0 1 =  2/4

(C) {2, 2, 2, 4, 5}
= 0 0 2 3 =  5/4

(D) {0, 2, 3, 4, 6}
= 3 1 1 3 =  8/4

(E) {-1, 1, 3, 5, 7}
= 4+2+2+4 =  12/4

The 3rd highest SD is A)

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Which of the following data sets has the third largest standard deviat

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Which of the following data sets has the third largest standard deviat

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