Author 
Message 
TAGS:

Hide Tags

Director
Joined: 10 Feb 2006
Posts: 647

The median annual household income in a certain community of
[#permalink]
Show Tags
Updated on: 12 Aug 2012, 08:17
Question Stats:
65% (00:46) correct 35% (01:01) wrong based on 632 sessions
HideShow timer Statistics
The median annual household income in a certain community of 21 households is $50,000. If the mean income of a household increases by 10% per year over the next 2 years, what will the median income in the community be in 2 years? (A) $50,000 (B) $60,000 (C) $60,500 (D) $65,000 (E) Cannot be determined
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
GMAT the final frontie!!!.
Originally posted by alimad on 21 Jun 2008, 21:01.
Last edited by Bunuel on 12 Aug 2012, 08:17, edited 1 time in total.
Edited the question and added the OA.




Math Expert
Joined: 02 Sep 2009
Posts: 47983

Re: Median
[#permalink]
Show Tags
12 Aug 2012, 08:27
nikhil007 wrote: nmohindru wrote: The median annual household income in a certain community of 21 households is $50,000. If the mean income of a household increases by 10% per year over the next 2 years, what will the median income in the community be in 2 years?
(A) $50,000 (B) $60,000 (C) $60,500 (D) $65,000 (E) Cannot be determined
Should be e)
Mean increasing by certain % doesnt mean that median should increase by same %.
Median will only increase by same % if all data point move ahead by same % but increase of mean does not guarantee that all data points are moving by same % as well. Hi, I am a bit confused now, I thought this was the rule.. " If we increase or decrease each term in a set by the same percent: Mean will increase or decrease by the same percent. SD will increase or decrease by the same percent. so by that if mean increase by 10%, shouldn't all data points move by 10%..? By the way, above rule was also Highlighted in one of the post by Bunuel Here psquestionsaboutstandarddeviation85897.htmlam I missing a point here? can someone please explain the concept here? Reverse of this property is not true: if the mean increases by a certain percent it doesn't necessarily mean that each term increases by the same percent. Consider the following set: {1, 2, 3} > mean=median=2 and sum=6. Now, if we increase the mean by 100%, we increase the sum by 100%, so it'll become 12. But new set can be {0, 0, 12}: the third element increased and the first two elements decreased or {2, 2, 8}: the first and the third elements increased and the second remained the same... You can apply the same logic to the question at hand. Answer: E.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




SVP
Joined: 04 May 2006
Posts: 1774
Schools: CBS, Kellogg

Re: Median
[#permalink]
Show Tags
21 Jun 2008, 21:44
alimad wrote: The median annual household income in a certain community of 21 households is $50,000. If the mean income of a household increases by 10 % / year over the next 2 years, what will be the median income in the community be in 2 years?
50,000 60,000 60,500 65,000 cannot be determined.
Please respond with your answers. thanks I think E, I find no connection btw the increase and the median!
_________________
GMAT Club Premium Membership  big benefits and savings



Director
Joined: 12 Jul 2008
Posts: 511
Schools: Wharton

Re: Median
[#permalink]
Show Tags
21 Jul 2008, 11:45
sondenso wrote: alimad wrote: The median annual household income in a certain community of 21 households is $50,000. If the mean income of a household increases by 10 % / year over the next 2 years, what will be the median income in the community be in 2 years?
50,000 60,000 60,500 65,000 cannot be determined.
Please respond with your answers. thanks I think E, I find no connection btw the increase and the median! I agree on E. The median could change depending on which incomes grow and by how much. For example, all incomes could grow by 10% each, meaning the median would also grow by 10%. Or the lowest income could grow by a huge number, moving it into the top half of incomes, which would completely change the median.



Senior Manager
Joined: 06 Apr 2008
Posts: 390

Re: Median
[#permalink]
Show Tags
21 Jul 2008, 23:19
Should be e)
Mean increasing by certain % doesnt mean that median should increase by same %.
Median will only increase by same % if all data point move ahead by same % but increase of mean does not guarantee that all data points are moving by same % as well.



Manager
Joined: 04 Dec 2011
Posts: 67

Re: Median
[#permalink]
Show Tags
12 Aug 2012, 08:08
nmohindru wrote: Should be e)
Mean increasing by certain % doesnt mean that median should increase by same %.
Median will only increase by same % if all data point move ahead by same % but increase of mean does not guarantee that all data points are moving by same % as well. Hi, I am a bit confused now, I thought this was the rule.. " If we increase or decrease each term in a set by the same percent: Mean will increase or decrease by the same percent. SD will increase or decrease by the same percent. so by that if mean increase by 10%, shouldn't all data points move by 10%..? By the way, above rule was also Highlighted in one of the post by Bunuel Here psquestionsaboutstandarddeviation85897.htmlam I missing a point here? can someone please explain the concept here?
_________________
Life is very similar to a boxing ring. Defeat is not final when you fall down… It is final when you refuse to get up and fight back!
1 Kudos = 1 thanks Nikhil



Manager
Joined: 04 Dec 2011
Posts: 67

Re: Median
[#permalink]
Show Tags
13 Aug 2012, 00:34
Bunuel wrote: Reverse of this property is not true: if the mean increases by a certain percent it doesn't necessarily mean that each term increases by the same percent.
Consider the following set: {1, 2, 3} > mean=median=2 and sum=6. Now, if we increase the mean by 100%, we increase the sum by 100%, so it'll become 12. But new set can be {0, 0, 12}: the third element increased and the first two elements decreased or {2, 2, 8}: the first and the third elements increased and the second remained the same...
You can apply the same logic to the question at hand.
Answer: E.
Wow thats an usefull insight..Kudos..!!
_________________
Life is very similar to a boxing ring. Defeat is not final when you fall down… It is final when you refuse to get up and fight back!
1 Kudos = 1 thanks Nikhil



Manager
Joined: 28 Feb 2012
Posts: 112
Concentration: Strategy, International Business
GPA: 3.9
WE: Marketing (Other)

Re: The median annual household income in a certain community of
[#permalink]
Show Tags
16 Aug 2012, 22:48
Answer is E, because there are different numbers in the set and we are not sure which side of the numbers in the set will be increased so the mean is increase by 10%. It could be the case that small number of higher end incomes increased a little or many low end incomes increased  it cannot be identified.
_________________
If you found my post useful and/or interesting  you are welcome to give kudos!



Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1355
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs

Re: The median annual household income in a certain community of
[#permalink]
Show Tags
18 Aug 2012, 18:55
+1 E For example, if the highest value increase enough to increase in 10% the mean, the median will be the same. Other scenario is that every value increases in 10%, including the median. We cannot determine the new median.
_________________
"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."
My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/myirlogbookdiary133264.html
GMAT Club Premium Membership  big benefits and savings



Retired Moderator
Joined: 17 Sep 2013
Posts: 369
Concentration: Strategy, General Management
WE: Analyst (Consulting)

Re: The median annual household income in a certain community of
[#permalink]
Show Tags
15 Apr 2014, 13:34
But here the It is clearly mentioned that it is the mean income of a household..So here the mean refers to the average rise in income of the household members and not the mean of the incomes of the cimmunity..I think it is a typo error or I am missing something here... Correct me if I am wrong
_________________
Appreciate the efforts...KUDOS for all Don't let an extra chromosome get you down..



Director
Status: Everyone is a leader. Just stop listening to others.
Joined: 22 Mar 2013
Posts: 871
Location: India
GPA: 3.51
WE: Information Technology (Computer Software)

Re: The median annual household income in a certain community of
[#permalink]
Show Tags
15 Apr 2014, 13:47
JusTLucK04 wrote: But here the It is clearly mentioned that it is the mean income of a household..So here the mean refers to the average rise in income of the household members and not the mean of the incomes of the cimmunity..I think it is a typo error or I am missing something here... Correct me if I am wrong We can not determine the median income from provided data. The median annual household income in a certain community of 21 households is $50,000. If the mean income of a household increases by 10% per year over the next 2 years, what will the median income in the community be in 2 years? As we do not know that distribution of income is uniform we can not conclude that median = mean from provided data we got that 11th household is earning $50,000 Let mean = x increase by 10% for next 2 years... we do not whether every house hold income has increased or few has increased or for few remain constant or reduced.. its easy to get 10% rise in mean by just increasing income for few households ..thus we can not construct data set and we can not get median. Answer is E.
_________________
Piyush K
 Our greatest weakness lies in giving up. The most certain way to succeed is to try just one more time. ― Thomas A. Edison Don't forget to press> Kudos My Articles: 1. WOULD: when to use?  2. All GMATPrep RCs (New) Tip: Before exam a week earlier don't forget to exhaust all gmatprep problems specially for "sentence correction".



Retired Moderator
Joined: 17 Sep 2013
Posts: 369
Concentration: Strategy, General Management
WE: Analyst (Consulting)

Re: The median annual household income in a certain community of
[#permalink]
Show Tags
15 Apr 2014, 13:57
PiyushK wrote: JusTLucK04 wrote: But here the It is clearly mentioned that it is the mean income of a household..So here the mean refers to the average rise in income of the household members and not the mean of the incomes of the cimmunity..I think it is a typo error or I am missing something here... Correct me if I am wrong We can not determine the median income from provided data. The median annual household income in a certain community of 21 households is $50,000. If the mean income of a household increases by 10% per year over the next 2 years, what will the median income in the community be in 2 years? As we do not know that distribution of income is uniform we can not conclude that median = mean from provided data we got that 11th household is earning $50,000 Let mean = x increase by 10% for next 2 years... we do not whether every house hold income has increased or few has increased or for few remain constant or reduced.. its easy to get 10% rise in mean by just increasing income for few households ..thus we can not construct data set and we can not get median. Answer is E. Bahh..My bad..I read it extremely wrongly. ...I was referring to the income rise from household members.. Don't know where did that come from..Guess I did better
_________________
Appreciate the efforts...KUDOS for all Don't let an extra chromosome get you down..



SVP
Joined: 06 Nov 2014
Posts: 1888

Re: The median annual household income in a certain community of
[#permalink]
Show Tags
14 May 2015, 11:07
E. Mean and median aren't interchangeable. The mean can have a very different value from the median if there are many households with very high or low incomes. Without the value of the mean provided, there's no way to predict what it will be.



Intern
Joined: 20 Jul 2017
Posts: 4

Re: The median annual household income in a certain community of
[#permalink]
Show Tags
25 Jul 2017, 01:14
The answer is E. The mean can be changed by changing one or more observations. As correctly pointed out in posts above, 10% increase in mean over two years doesn't mean that each observation increases by 10%. Therefore median may or may not be 50,000 after two years. When you assume the theory that each observation is changing by 10% per year, answer comes out to be $60,500.



NonHuman User
Joined: 09 Sep 2013
Posts: 7754

Re: The median annual household income in a certain community of
[#permalink]
Show Tags
01 Aug 2018, 09:03
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: The median annual household income in a certain community of &nbs
[#permalink]
01 Aug 2018, 09:03






