In life we often take things for granted and assume most things exhibit normal behavior or distribution. People should be wary of the risk arising from the tails in the distribution because they can have devastating impacts, especially in these times when we are seeing tail risk’s being played out more often then we would like whether it is extreme climate change related, volatility in financial markets, occurrence of a global pandemic, geopolitics etc. To understand what constitutes a tail risk we need to understand what is “normal”?
Let’s add some statistics to the mix and understand what a Normal distribution is with a generic example, the height of adult men in the US. On average an adult Male in US is 70 inches tall with a standard deviation of 3 inches. If we were plot the heights of every male in the US, it would like the curve below which we call as a normal distribution. What you can deduce from a normal distribution is 99.7% of population will be between +/- 3 standard deviations from the mean/average. In this case of 99.7% of adult males in the US is between 61 to 79 inches (+/- 3 standard deviation from mean). The mean and median in a normal distribution are identical, for the uninitiated you might be wondering what is median. We will get to what a median means but the tails in a normal distribution are the 1-2% towards the end of either side of a normal distribution. In this example for instance there are people who are taller than 79 inches and shorter than 61 inches but they represent 0.3% of the population and there is no evidence that we are seeing a sudden surge/spike in adult males taller than 79 inches or shorter than 61 inches.
Now let’s understand Median, one of the most underutilized and misunderstood metrics in Corporate America. In fact you will often see jokes like this “The median and the mode walked into a bar. The bartender asks, "Where's your other friend". The median says, "We don't like him anymore. He's mean."
Median by definition is the middle number or observation in a sorted list of observations, its value is not swayed by the outliers in a distribution. Mean is simple average of all observations in the list, its value is swayed by outliers (if they exist) in a distribution. The best example that illustrates the median is the example of US Household income distribution. As you can see from the chart below, that the US Income Household distribution is not a normal one as it is heavily skewed with a long right tail.
This distribution is “skewed” because, the household income of 50% of the households on the right side of the middle household in US (that earns $67,463/ year) is so high that it has moved the average household income 50% higher than the median to $96,995. This is often misunderstood because we assume all distributions are normal and averages are everything, so in this case people assume 50% of households in US make more than $96,995 which is not true because only 33% of households in the US make more than that the average. This “skew” here is referred to in more general terms as Income Inequality.
In Corporate America whether you work in Marketing, Sales, Finance, Technology, Compliance etc. a clear understanding of the distribution, mean and median metrics of any of your customer’s usage data can help to better allocate resources in areas such targeting & segmentation, sales planning, troubleshooting issues/outages, pin pointing malicious intent etc. “Income Inequality” though is a critical problem in the US with the gap between the median and mean income continuing to widen. I believe the solutions to reducing the gap lies in the better understanding of the chart itself with a goal of making the median equal to mean of $96,995 [Propping income of low income households]. I am not proposing you take care of the outliers by taxing them more, I believe that move will kill productivity and move mean to the median of $67,463 [dropping income of households], a backward step stifling innovation in this country. There are solutions that can be developed and implemented when the best minds in the private and public domain come together, for instance wouldn't it be an amazing challenge to find the right strategy, tactics and incentives that would prop up the income of the 17% households that are between $67,463 (median) and $96,995 (mean)?