Stat Unit

Income as a Skewed Distribution

A good example of a positively skewed distribution in the United States is income. The mean income in this country is considerably higher than the mode or the median. This is because there are a number of individuals with extremely large incomes -- Bill Gates, Paul Allen, Donald Trump, Ross Perot, Oprah Winfrey, etc. And, as we have already learned, the mean is pulled in the direction of these large incomes.

If we were to use the mean income to represent "typical income" in this country, the majority of individuals would have incomes BELOW the mean. Why? When a distribution is positively skewed, the mean is the largest measure of central tendency; the mode is the smallest measure of centraltendency; and the median falls between these two measures. Remember, the mean is pulled in the direction of the extreme incomes -- thereby greatly increasing its magnitude. On the other hand, the mode is the high point on the distribution, and in a positively skewed distribution of incomes, the high point falls on the low side. Regardless of the distribution's shape, the median remains the point that divides the distribution into two equal halves -- making it a true "middle" even for any distribution. The mean's sensitivity to extreme values ensures that it will be larger than either the mode or median in a positively skewed distribution. On the other hand, the mode may actually be too small in value -- thereby underestimating the distribution's center. But with the median representing the true middle with 50 percent of the incomes below it and 50 percent of the incomes above it, we can be fairly certain we are getting an accurate picture of a distribution's middle. This stability across all distribution shapes makes the median a better choice for central tendency when a distribution is heavily skewed.

In short, when a distribution is positively skewed, the mode presents a less prosperous picture of income earnings and the mean presents a more prosperous picture of income earnings for individuals in this country. However, the median presents the most accurate picture of income earnings.