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You underestimate just how dumb the average person is I think.
I always think of the George Carlin quote: “Think of how stupid the average person is, and realize half of them are stupider than that.”
That's not how "average" (the mean value) works. You need the median to tell if 50% are less intelligent. The funny part is, that intellegence is measured via IQ, which is itself standard normalized, so that the mean value lies at the center of your distribution (100 IQ). So I could just stfu.
Mean and median tend to be roughly equivalent in large sample sizes though.
It depends on the distribution. In most cases you get a normal distribution due to the central limit theorem (in probability theory). In general, the mean and median could differ a lot, even at big sample sizes. Look at the distribution of the income for example.