A fundamental task in many statistical analyses is to characterize the location and variability of a data set. A further characterization of the data includes skewness and kurtosis. Most often, the median is used as a measure of central tendency when data sets are skewed. Skewness is a measure of symmetry, or more precisely, the lack of symmetry. A distribution, or data set, is symmetric if it looks the same to the left and right of the center point. The skewness for a normal distribution is zero, and any symmetric data should have a skewness near zero. Normal distributions will have a skewness value of approximately zero. Right-skewed distributions will have a positive skewness value; left-skewed distributions will have a negative skewness value. Typically, the skewness value will range from negative 3 to positive 3. Two examples of skewed data sets are salaries within an organization and monthly prices of homes for sale in a particular area. Negative values for the skewness indicate data that are skewed left and positive values for the skewness indicate data that are skewed right. By skewed left, we mean that the left tail is heavier than the right tail. Similarly, skewed right means that the right tail is heavier than the left tail. Some measurements have a lower bound and are skewed right. The metric that indicates the degree of asymmetry is called, simply, skewness. Skewness often results in situations when a natural boundary is present. For example, in reliability studies, failure times cannot be negative. Kurtosis is a measure of whether the data are peaked or flat relative to a normal distribution. That is, data sets with high kurtosis tend to have a distinct peak near the mean, decline rather rapidly, and have heavy tails. Data sets with low kurtosis tend to have a flat top near the mean rather than a sharp peak. A uniform distribution would be the extreme case. The standard normal distribution has a kurtosis of zero. Positive kurtosis indicates a "peaked" distribution and negative kurtosis indicates a "flat" distribution.

Use radio buttons to select distribution type and parameter displayed onthe graph. You can select "Show Gaussian distribution" to graph Gaussian distribution in the same coordinates.