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.
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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.

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?
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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.
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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
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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
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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.

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)

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.

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
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