Distributions are graphical depictions of statistical probabilities. Graphs of statistical distributions resemble mountains. The lines on the far left and far right sides of the graph are called tails. Distributions become skewed when one tail is longer than the other. When the skew is positive, the longer tail is on the side of the graph with positive numbers. When the skew is negative, the longer tail is on the side of the graph with negative numbers. An example of a skewed distribution could involve the unemployment rate. Some people might not have ever held a job -- if for example, they were incarcerated for most of their lives -- which skews the unemployment rate up. Skewed distributions are parts of research techniques that still can give accurate data -- especially when the distributions are not skewed too far.
Extremely skewed distributions can lead to misleading statistics, since the skewed distribution can drive an average up or down. For example, the average income of a particular society may be low, but a handful of people might have high earnings, which skews the average income of the society upward. Badly skewed data can lead to incorrect results, which is a disadvantage of skewed distributions.
In most distributions, the mean is easy to find by looking at the middle. The mean is the average of the distribution. However, with a much-skewed distribution, the mean is not necessarily in the middle, making the mean more difficult to find. Many statistical techniques rely on the statistical mean of the distribution, which can make skewed distributions difficult to work with.
A logarithm is the power at which a base must be to reach a specific number. For example, when the number is 1000 and the base is 10, the logarithm is 3, since 10 to the power of 3 is 1,000. With powers, each number represents the number of times the mathematician multiplies the base number by itself. Since the skewed variables are usually lognormal, the logarithm of the random variable is normal. Normal distribution is symmetrical and has a bell-shaped curve. Normal distributions allow people to more accurately predict variables. For example, battery lifetime has a normal distribution, meaning that a battery might last 40 hours on average and have a deviation of one hour, meaning the battery could run out of energy in 39 hours or 41 hours. The advantage of this is that statisticians can generate a range that predicts a set of variables.
Many people do not understand statistics. Pundits can often present statistics in the realm of politics in a way that can support their otherwise erroneous argument. However, those seeking to skew public opinion might view this as an advantage. People do not always understand how skewed distributions work, so a pundit could present statistics that seem accurate, but actually are not because of the skewed distribution.