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

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

The median annual household income in a certain community of [#permalink]
21 Jun 2008, 20:01

4

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

25% (medium)

Question Stats:

62% (01:51) correct
38% (00:58) wrong based on 305 sessions

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?

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! _________________

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.

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.

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%..?

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?

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%..?

am 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.

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!

Re: The median annual household income in a certain community of [#permalink]
16 Aug 2012, 21:48

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!

Re: The median annual household income in a certain community of [#permalink]
18 Aug 2012, 17:55

+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."

Re: The median annual household income in a certain community of [#permalink]
15 Apr 2014, 12:34

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..

Re: The median annual household income in a certain community of [#permalink]
15 Apr 2014, 12:47

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".

Re: The median annual household income in a certain community of [#permalink]
15 Apr 2014, 12:57

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..

Re: The median annual household income in a certain community of [#permalink]
11 May 2015, 16:54

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. _________________

Re: The median annual household income in a certain community of [#permalink]
14 May 2015, 10:07

Expert's post

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. _________________

Janielle Williams Customer Support | Optimus Prep

gmatclubot

Re: The median annual household income in a certain community of
[#permalink]
14 May 2015, 10:07

On September 6, 2015, I started my MBA journey at London Business School. I took some pictures on my way from the airport to school, and uploaded them on...

When I was growing up, I read a story about a piccolo player. A master orchestra conductor came to town and he decided to practice with the largest orchestra...

Today was the last day of our three-week Launch, that ended on a high note with a drinks and dance reception. The class decided to shift the party outside...

There is one comment that stands out; one conversation having made a great impression on me in these first two weeks. My Field professor told a story about a...