The median annual household income in a certain community of

Question

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

(A) $50,000 
(B) $60,000 
(C) $60,500 
(D) $65,000
(E) Cannot be determined

Bunuel · Accepted Answer

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.

sondenso · Answer

I think E, I find no connection btw the increase and the median!

zonk · Answer

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.

nmohindru · Answer

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.

nikhil007 · Answer

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 ps-questions-about-standard-deviation-85897.html am I missing a point here? can someone please explain the concept here?

nikhil007 · Answer

Wow thats an usefull insight..Kudos..!!

ziko · Answer

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.

metallicafan · Answer

+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.

JusTLucK04 · Answer

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

PiyushK · Answer

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 % / 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

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.

JusTLucK04 · Answer

Bahh..My bad..I read it extremely wrongly. :toilet

...I was referring to the income rise from household members.. :yikes

Don't know where did that come from..Guess I did :sleep

better

OptimusPrepJanielle · Answer

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.

Kavya123 · Answer

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.

hulk007 · Answer

"If the mean income of  a  household ..." It doesnt say if the mean annual income increases by 10%. 
I believe this question is meant to throw off people for not following the thumb rule blindly just because it mentions median,mean & % increase.

Doesnt the question mean, 10% for each family , thus increasing each value in the set by 10% , thus increasing the median also by 10% eventually being 60,500 ?

( not following the thumb rule here , just going by logic)

hulk007 · Answer

yes i felt the same.

"If the mean income of a household ..." It doesnt say if the mean annual income increases by 10%. 
I believe this question is meant to throw off people for not following the thumb rule blindly just because it mentions median,mean & % increase.

Doesnt the question mean, 10% for each family , thus increasing each value in the set by 10% , thus increasing the median also by 10% eventually being 60,500 ?

( not following the thumb rule here , just going by logic)

hulk007 · Answer

"If the mean income of a household ..." It doesnt say if the mean annual income increases by 10%. 
I believe this question is meant to throw off people for not following the thumb rule blindly just because it mentions median,mean & % increase.

Doesnt the question mean, 10% for each family , thus increasing each value in the set by 10% , thus increasing the median also by 10% eventually being 60,500 ?

( not following the thumb rule here , just going by logic)

masoomjnegi · Answer

Increase in mean value of a set has no direct relation with the increase in median value of the set. Here, we are given the increase in the mean value but we don’t know if the increase is because of change in just 1 value of because of the change in all values. Hence, we can’t determine the change in median. Hence, E is the answer.

hulk007 · Answer

"If the mean income of  a  household ..." It doesnt say if the mean annual income increases by 10%. 
Doesnt the question mean, 10% for each family , thus increasing  each value in the set  by 10%

i say again , i think this question was designed to throw off people for not blindly applying/ignoring the thumb rule .

ScottTargetTestPrep · Answer

It’s impossible to determine the median household income from the information given. For example, if the reason the mean household income increases by 10% per year over the next 2 years is because the annual income of every household increases by 10% per year over the next 2 years, then the median household income would also increases by 10% per year over the next 2 years, to 50,000 x 1.1 x 1.1 = $60,500. However, it’s possible that only the household with the highest annual income increases by a tremendous amount each year for the next 2 years, such that the mean household income for the community increases by 10% per year over the next 2 years. In that case, the median household income would stay the same at the end of the 2 years, i.e., at $50,000.

Answer: E

The median annual household income in a certain community of

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