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Question: 

For persons aged 25 and over in the US would the average
or the median be higher for income?

I'm not sure how to answer this.

If I assume that the wage increases with age, and that every age range is equally represented, then perhaps I'll (extremely roughly) have a graph like this :

enter image description here

There the y axis is the wage,and the x axis is representing age.

Then the median wage is where half people earn more, and half of the people earn less. And the mean wage is the average wage that people will earn.

In this case the mean will be greater than the median.

But I'm not sure if this is an appropriate way to consider this problem, or how to explain it clearly.

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    $\begingroup$ Hint: draw a histogram of what you think a random sample of these incomes would look like. $\endgroup$
    – whuber ♦
    Commented Oct 20, 2017 at 21:22
  • $\begingroup$ If age were uniformly distributed between 25 & 75, & income were an exact linear function of age, what distribution would income have? An asymmetric one? $\endgroup$
    – Scortchi ♦
    Commented Oct 20, 2017 at 21:24
  • $\begingroup$ I'm not sure I follow , and I don't know what age ranges I'm meant to be doing either I just have " over 25 ". So I've presumed that people are working until they're 70 and that their wage increases up until then. Though It wouldn't increase at the same rate etc, I've made it as basic as possible. $\endgroup$
    – baxx
    Commented Oct 20, 2017 at 21:24
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    $\begingroup$ Go back to whuber's hint. Imagine a random sample of over-25-year-olds. You surely have a better idea what the distribution of their incomes would look like than about the relation between their ages & their incomes, & the former is all you're being asked about. $\endgroup$
    – Scortchi ♦
    Commented Oct 20, 2017 at 21:34
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    $\begingroup$ Hint: Why does age matter at all? Suppose they said "adults" instead of 25+. Would that change your answer? And, again, look at @whuber 's hint. $\endgroup$
    – Peter Flom
    Commented Oct 20, 2017 at 22:04

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Yes, the average is higher than the median, and the reason is that the distribution of incomes is not symmetric.

In fact, symmetric distributions have the same value for the mean and the median. But the income in the US is not symmetric: in fact you have a few people making a lot of money and a lot of people making little money. So that the median is pretty low, compared to the mean: the mean is affected by the rich guys but the median is not.

About your argument, it is probably true that the income is correlated with age but that's not necessarily what makes the distribution asymmetric.

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