Hey, could you please help me in understanding the below question how to solve it
Q-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
Standard Deviation
This topic has expert replies
- nsharma215
- Newbie | Next Rank: 10 Posts
- Posts: 4
- Joined: Fri Feb 21, 2014 6:16 am
- Followed by:1 members
- theCodeToGMAT
- Legendary Member
- Posts: 1556
- Joined: Tue Aug 14, 2012 11:18 pm
- Thanked: 448 times
- Followed by:34 members
- GMAT Score:650
A {30,50,70,90,110}
B {-20, -10,0,10,20}
C {30,35,40,45,50}
Mean of A = 350/5 = 70
mean of B = 0
Mean of C = 200/5 = 40
The farther the added value is from mean, the more is S.D
So, B,C,A
{E}?
B {-20, -10,0,10,20}
C {30,35,40,45,50}
Mean of A = 350/5 = 70
mean of B = 0
Mean of C = 200/5 = 40
The farther the added value is from mean, the more is S.D
So, B,C,A
{E}?
R A H U L
- nsharma215
- Newbie | Next Rank: 10 Posts
- Posts: 4
- Joined: Fri Feb 21, 2014 6:16 am
- Followed by:1 members
Answer is correct thanks.
So take away is that Mean is 0 and 100 is getting add in SD
and 100(SD) is far from the 0(mean)
So take away is that Mean is 0 and 100 is getting add in SD
and 100(SD) is far from the 0(mean)
- GMATinsight
- Legendary Member
- Posts: 1100
- Joined: Sat May 10, 2014 11:34 pm
- Location: New Delhi, India
- Thanked: 205 times
- Followed by:24 members
nsharma215 wrote:Hey, could you please help me in understanding the below question how to solve it
Q-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
Standard Deviation is the representation of Average Deviation of the terms in the given Set from the Mean of the set.
Which means "the new Term is added to set" at a greater difference from the Mean of the set will increase the the standard deviation by a greater amount
If we compare the Standard Deviation of the sets given then we realize that
SD of C < SD of B = SD of A [Because in set A and B the consecutive terms are separated by a common difference 20 whereas the difference between consecutive terms of Set C are at a deviation of 5]
100 is farthest from mean of B therefore Mean of B will be changed greatest after including 100 in set
This eliminated Options A, B and C
Between Set A and C, Set C has much lower standard deviation than Set A but after including 100 It will increase for both Sets but the substantial change will be noticed in SET C because 100 falls within the terms of Set A therefore
after including 100 in each set
SD of C > SD of A
Therefore the correct Order of Change in SD will be B > C > A
Answer: Option E
Last edited by GMATinsight on Mon Jul 21, 2014 6:27 am, edited 1 time in total.
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
- GMATinsight
- Legendary Member
- Posts: 1100
- Joined: Sat May 10, 2014 11:34 pm
- Location: New Delhi, India
- Thanked: 205 times
- Followed by:24 members
One can also verify by inputting the values of the sets in on the page whose link is as follows
https://easycalculation.com/statistics/s ... iation.php
https://easycalculation.com/statistics/s ... iation.php
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
For the purposes of the GMAT, 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.
------------------------------
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
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.
------------------------------
So, for this question, we have: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
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
GMAT/MBA Expert
- ceilidh.erickson
- GMAT Instructor
- Posts: 2095
- Joined: Tue Dec 04, 2012 3:22 pm
- Thanked: 1443 times
- Followed by:247 members
With Standard Deviation questions on the GMAT, you will never be asked to calculate the actual standard deviation, because that involves some complex computation. To actually calculate, we'd find the difference between each term and the mean, then square that, then find the average of all of those, and square root that. For reference: https://en.wikipedia.org/wiki/Standard_d ... c_examples
The GMAT will never ask you to do that! The most that they can ask is that you understand that high SD means the data is spread out far from the mean, and a low SD means that most data is clustered closely around the mean. Whenever you see a SD question, just translate it as "how much is the data spread out?"
When you add 100 to each set, the further 100 is from the mean, the more it will "spread" the data out from the mean.
The GMAT will never ask you to do that! The most that they can ask is that you understand that high SD means the data is spread out far from the mean, and a low SD means that most data is clustered closely around the mean. Whenever you see a SD question, just translate it as "how much is the data spread out?"
When you add 100 to each set, the further 100 is from the mean, the more it will "spread" the data out from the mean.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
GMAT/MBA Expert
- ceilidh.erickson
- GMAT Instructor
- Posts: 2095
- Joined: Tue Dec 04, 2012 3:22 pm
- Thanked: 1443 times
- Followed by:247 members
For more on Standard Deviation, see:
https://www.beatthegmat.com/call-for-hel ... tml#545420
https://www.beatthegmat.com/standard-dev ... tml#680908
https://www.beatthegmat.com/call-for-hel ... tml#545420
https://www.beatthegmat.com/standard-dev ... tml#680908
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Here are a few more practice questions where we can apply the concept of "average distance from the mean" as an approximation for Standard Deviation:
https://www.beatthegmat.com/standard-dev ... 74384.html
https://www.beatthegmat.com/standard-dev ... 69584.html
https://www.beatthegmat.com/range-and-sd-t89159.html
Cheers,
Brent
https://www.beatthegmat.com/standard-dev ... 74384.html
https://www.beatthegmat.com/standard-dev ... 69584.html
https://www.beatthegmat.com/range-and-sd-t89159.html
Cheers,
Brent
- nsharma215
- Newbie | Next Rank: 10 Posts
- Posts: 4
- Joined: Fri Feb 21, 2014 6:16 am
- Followed by:1 members
- Anaira Mitch
- Master | Next Rank: 500 Posts
- Posts: 235
- Joined: Wed Oct 26, 2016 9:21 pm
- Thanked: 3 times
- Followed by:5 members
Brent@GMATPrepNow wrote:For the purposes of the GMAT, 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.
------------------------------So, for this question, we have: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
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
Amazing explanation Brent.
-
- Junior | Next Rank: 30 Posts
- Posts: 15
- Joined: Fri Jan 20, 2017 8:11 pm
Hey Brent,
I am confused with the language of this question ( the absolute increase in their Standard Deviation, from largest to smallest? )
Is this question asking to arrange the S.D of all set in descending order?
I totally understand the concept of S.D, and looking at the given set and their spread I can easily see that first set has largest S.D and last set has the least S.D.
So if this question is asking about arranging the S.D in descending order then it would have been a,b,c.
But this is not the answer.
what is absolute increase in this case?
As when we calculate S.D of each set (which is not required ,But I calculated out of curiosity ) are:
a) 31.6
b) 15.8
c) 7.9
why are you subtracting each value of mean from 100?
I am confused with the language of this question ( the absolute increase in their Standard Deviation, from largest to smallest? )
Is this question asking to arrange the S.D of all set in descending order?
I totally understand the concept of S.D, and looking at the given set and their spread I can easily see that first set has largest S.D and last set has the least S.D.
So if this question is asking about arranging the S.D in descending order then it would have been a,b,c.
But this is not the answer.
what is absolute increase in this case?
As when we calculate S.D of each set (which is not required ,But I calculated out of curiosity ) are:
a) 31.6
b) 15.8
c) 7.9
why are you subtracting each value of mean from 100?
GMAT/MBA Expert
- Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
Hi Neha,neha shekhawat wrote:Hey Brent,
I am confused with the language of this question ( the absolute increase in their Standard Deviation, from largest to smallest? )
Is this question asking to arrange the S.D of all set in descending order?
I totally understand the concept of S.D, and looking at the given set and their spread I can easily see that first set has largest S.D and last set has the least S.D.
So if this question is asking about arranging the S.D in descending order then it would have been a,b,c.
But this is not the answer.
what is absolute increase in this case?
As when we calculate S.D of each set (which is not required ,But I calculated out of curiosity ) are:
a) 31.6
b) 15.8
c) 7.9
why are you subtracting each value of mean from 100?
"Is this question asking to arrange the S.D of all set in descending order?" is incorrect. The question does not ask this.
This question asks to arrange the ABSOLUTE INCREASE IN THE VALUES OF S.D of all set in descending order?
We need not be bothered about the values of the SDs of the three sets.
Say, currently the SDs of Sets A, B and C are a, b, and c, respectively. We need not know which value among a, b, and c is the largest and which is rhe smallest.
We are concerned with what happens when a new entrant '100,' is included in each set.
Say after the inclusion of '100,' the new SDs of three sets A, B, and C are (a + a'), (b + b'), and (c + c'), respectively; where a', b' and c' are the absolute increase in respective SD values.
The question asks us to arrange the values of a', b' and c' in descending order.
Hope this helps!
Relevant book: Manhattan Review GMAT Sets & Statistics Guide
-Jay
_________________
Manhattan Review GMAT Prep
Locations: New York | Singapore | London | Dubai | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
-
- Junior | Next Rank: 30 Posts
- Posts: 15
- Joined: Fri Jan 20, 2017 8:11 pm
Thanks jay
I just realized that I missed the sentence (If number 100 is included in each of these sets) while reading the question.I straight away jumped on the sets.I have to pay more attention while reading such questions now.
I just realized that I missed the sentence (If number 100 is included in each of these sets) while reading the question.I straight away jumped on the sets.I have to pay more attention while reading such questions now.
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
This is such a great lesson to learn from this problem. On the GMAT, of all places, is the devil IS in the details: subtle misreadings are deadly, and many of the questions are written to ENCOURAGE such misreadings!neha shekhawat wrote:Thanks jay
I just realized that I missed the sentence (If number 100 is included in each of these sets) while reading the question.I straight away jumped on the sets.I have to pay more attention while reading such questions now.