GRE Prep 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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sets A, B and C are shown below. If number 100 is included in each of
[#permalink]
20 Sep 2021, 08:55
20 Sep 2021, 08:55
Expert Reply
3
Bookmarks
00:00
Question Stats:
70% (01:27) correct
30% (01:24) wrong based on 10 sessions
Hide Show timer Statistics
Sets A, B and C are shown below. If number 100 is included in each of these sets, which of the following represents the correct ordering of the sets in terms of the absolute increase in their standard deviation, from largest to smallest?
A {30, 50, 70, 90, 110}, B {-20, -10, 0, 10, 20}, C {30, 35, 40, 45, 50}
(A) A, C, B
(B) A, B, C
(C) C, A, B
(D) B, A, C
(E) B, C, A
A {30, 50, 70, 90, 110}, B {-20, -10, 0, 10, 20}, C {30, 35, 40, 45, 50}
(A) A, C, B
(B) A, B, C
(C) C, A, B
(D) B, A, C
(E) B, C, A
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Sets A, B and C are shown below. If number 100 is included in each of
[#permalink]
20 Sep 2021, 09:01
20 Sep 2021, 09:01
1
Carcass wrote:
Sets A, B and C are shown below. If number 100 is included in each of these sets, which of the following represents the correct ordering of the sets in terms of the absolute increase in their standard deviation, from largest to smallest?
A {30, 50, 70, 90, 110}, B {-20, -10, 0, 10, 20}, C {30, 35, 40, 45, 50}
(A) A, C, B
(B) A, B, C
(C) C, A, B
(D) B, A, C
(E) B, C, A
A {30, 50, 70, 90, 110}, B {-20, -10, 0, 10, 20}, C {30, 35, 40, 45, 50}
(A) A, C, B
(B) A, B, C
(C) C, A, B
(D) B, A, C
(E) B, C, A
----ASIDE-------------------------
For the purposes of the GRE, it's sufficient to think of Standard Deviation as the Average Distance from the Mean.
Here's what I mean:
Consider these two sets: Set A {7,9,10,14} and set B {1,8,13,18}
The mean of set A = 10 and the mean of set B = 10
How do the Standard Deviations compare? Well, since the numbers in set B deviate the more from the mean than do the numbers in set A, we can see that the standard deviation of set B must be greater than the standard deviation of set A.
Alternatively, let's examine the Average Distance from the Mean for each set.
Set A {7,9,10,14}
Mean = 10
7 is a distance of 3 from the mean of 10
9 is a distance of 1 from the mean of 10
10 is a distance of 0 from the mean of 10
14 is a distance of 4 from the mean of 10
So, the average distance from the mean = (3+1+0+4)/4 = 2
B {1,8,13,18}
Mean = 10
1 is a distance of 9 from the mean of 10
8 is a distance of 2 from the mean of 10
13 is a distance of 3 from the mean of 10
18 is a distance of 8 from the mean of 10
So, the average distance from the mean = (9+2+3+8)/4 = 5.5
IMPORTANT: I'm not saying that the Standard Deviation of set A equals 2, and I'm not saying that the Standard Deviation of set B equals 5.5 (They are reasonably close however).
What I am saying is that the average distance from the mean can help us see that the standard deviation of set B must be greater than the standard deviation of set A.
More importantly, the average distance from the mean is a useful way to think of standard deviation. This model is a convenient way to handle most standard deviation questions on the GMAT.
------NOW ONTO THE QUESTION!!!---------------
So, for this question, we have:
Mean of set A = 70
Mean of set B = 0
Mean of set C = 40
100 is furthest away from the mean of 0 in set B, so this will cause the GREATEST change in standard deviation.
100 is next furthest away from the mean of 40 in set C, so this will cause the 2nd greatest change in standard deviation.
100 is closest to the mean of 70 in set A, so this will cause the LEAST change in standard deviation.
Answer: E
Cheers,
Brent
gmatclubot
Re: Sets A, B and C are shown below. If number 100 is included in each of [#permalink]
20 Sep 2021, 09:01
Moderators:
