Real life examples of probability distributions having negative or positive skew

Question

I am aware that in a negatively skewed distribution, we have that
Mode > Median > Mean, and that in normal distribution, we have that Mode=Median=Mean.

Can someone share real life examples of positively skewed and negatively skewed distributions?

Answer 1

1. Wealth/income distributions are skewed positively. This is what people mean in America when they say "the richest 0.1% hold 30% of the wealth." The mean wage is thus skewed up by those happy few, whereas the median wage/wealth is more like what an average American would face.

2. In the classes I have been in/taught, there tends to be a slight negative skew of the average. For example, in a class of $20$, if $19$ people get around the same score (say close to $85$, $\pm 5$) and the last person really struggled and gets a $0$, this will skew down the mean whereas the median/mode will still be a decent representation of the score.

3. In a stock portfolio, there are many long-term investors who have one "baby stock" that is their keep and hold, and they keep most of their money in mutual funds. Mutual funds tend to have low but steady growth whereas the stock may fluctuate based on the will of the masses. In this case, the stock could skew up or down the average rate of return on the portfolio.

Answer 2

Positively skewed distributions can be found, among other places, when you look at incomes, wealth, and other related quantities. Most people have a small-to-modest income, but there is a long tail in the positive direction, with a few people making millions or billions. Even though someone can have an income that exceeds the median by millions of dollars, nobody can have an income that is millions of dollars less than the median.

A nice example of a negatively skewed distribution would be the amount of time a pregnancy lasts before resulting in a live birth/delivery. Most pregnancies last close to full term (40 weeks), and very few last longer than that. At the other end, though, premature births can be successful (thanks to modern medicine) as early as 23-25 weeks. These are, however, much less common. This produces a long tail in the negative direction because, while a handful of babies are as much as 10-15 weeks early, none are 10-15 weeks late!

Do these examples answer your question?