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AlexHanson007 t1_j1h6719 wrote

Reply to comment by basketcase7 in Compared to your other family members, how would you rate yourself as a gift giver on a scale of 0-100? [OC] by GradientMetrics

It's a comparison against others, not an independent and absolute rating. Assuming our sample population is not biased and is a fair reflection of society, then it does have to be normally distributed.

What this graph is saying is that, compared to others, most people are better at something. That's not possible. That would be like having a race and saying most people finished in 3rd place (assuming there aren't joint finishes).

As someone else pointed out, this is an example of the Lake Wobegon effect.

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Elendur_Krown t1_j1hfuas wrote

Why would it have to be normally distributed?

In my eyes a non-biased relative comparison could end up with a whole host of distributions. A relative measure only means that you'll translate and perhaps rescale the original distribution.

Do you have a theorem or specific result to refer to?

I should also point out that the Lake Wobegon effect is at its most relevant when the underlying distribution is symmetric. Meaning that the average and the median are equivalent. This does hold for e.g. normal distributions. But if we allow for distributions with long smaller-than-mean tails, it would be possible that a majority are better than the mean.

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