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This is a question I recently saw on a test:

"Consider the following statement: More than 65% of the residents of Los Angeles earn less than the average wage for that city. Could this statement be correct? If so, how? If not, why not?"

The answer I put was that this statement could be correct because the mean isn't always centered perfectly, and nothing else (and I actually got full credit for this). After the test, however, I've had trouble understanding how the mean isn't always centered perfectly, because it evenly sums all the values and divides it by the number of values in the distribution. I think it could have something to do with skews and outliers, but I'm not completely sure.

Can somebody please explain this to me?

ahskdjfk
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    What would happen to the average wage if, say, Jeff Bezos were to move into the city? See https://stats.stackexchange.com/questions/2547/ for a closely related thread. – whuber Sep 24 '20 at 15:56
  • Check the distinction between the mean and the median of a population. – Xi'an Sep 24 '20 at 17:39
  • Average is meant to mean median. Not surprising as income is skewed. Classic problem of using terms without defining them. – AdamO Sep 24 '20 at 18:40
  • Closely related: https://stats.stackexchange.com/questions/2547. – whuber Nov 06 '20 at 16:45

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Don't confuse the "mean" with the "median". There are always half members on each side of the "median", not the "mean".

To illustrate, as an example, consider a group of 100 people, among them 35 have higher incomes, say, each has 1 million dollars per year, while other 65 have lower incomes, each has 0.1 million dollars per year. The mean (average) income for each person then is (35+6.5)/100 = 0.415 millions. Obviously, 65% of the group have their incomes below the mean.

user295357
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