Under real world conditions, probability distributions are usually skewed. The skewness of a distribution can be measured by most spreadsheet functions (eg SKEW in MS EXCEL) as a measure of how "normal" a particular distribution may be. For a normal distribution, the measure of skewness of course approximates zero.
Kurtosis is a measure of the "peakedness" of a distribution, and can be measured by the KURT function in EXCEL. A uniform distribution (described below) that describes an equal probability of outcomes will have a kurtosis of around 1.8, while a triangular distribution (also described below) is around 2.4. A distribution that has a skewness of around 0 and a kurtosis close to 3 should be considered to be a normal distribution.
The normal distribution is useful in determining the behaviour of many cost drivers in a project. For example, a construction engineer may wish to determine the number of construction delays, in days, which may be caused by extreme weather during July and August of any given year. The weather bureau provides the engineer with data on the number of extreme weather days over the past 30 years during the July-August period. Statistical analysis of the sample distribution provides that following information:
◼ Average: 10 days
◼ Standard deviation: 6 days
◼ Skew: 0.1
◼ Kurtosis: 2.8
The skew and kurtosis of the data indicates a normal distribution. Using standard statistical analysis, the engineer can establish a 95% confidence level for the sampling distribution that the average number of extreme weather days will be between 8 and 12 during any July and August construction period.