Page 254 - Six Sigma Demystified

234 Six SigMa DemystifieD

or housing prices, the median is a much better indicator of central ten-
dency.

• Standard deviation. The standard deviation provides an estimate of varia-
tion. In mathematical terms, it is the second moment about the mean. In
simpler terms, it is related to the average distance of the process observa-
tions from the mean.
• Skewness. The skewness provides a measure of the location of the mode (or
high point in the distribution) relative to the average. In mathematical
terms, it is the third moment about the mean. Symmetrical distributions, such
as the normal distribution, have a skewness of zero. When the mode is to
the left of the average, the skewness is negative; to the right, it is positive.

• Kurtosis. The kurtosis provides a measure of the “peakedness” of a distribu-
tion. In mathematical terms, it is the fourth moment about the mean. The
normal distribution has a kurtosis of 1. Distributions that are more peaked
have higher kurtoses.

If we know or can reliably assume the type of distribution to be applied to
the process, we can estimate the necessary parameters using sample data.
The binomial, Poisson, and exponential distributions require only a known
(or reliably estimated) average to define the distribution. These are one-param-
eter distributions, meaning that the remaining parameters (standard deviation,
skewness, and kurtosis) are defined solely by its mean. The normal distribution
requires two parameters (the mean and the standard deviation) because the
skewness and kurtosis are defined to produce its characteristic bell shape.
The Johnson and Pearson distributions require estimates of up to four param-
eters for a given distribution shape. These methods are best applied using sta-

tistical software to fit the distributional curves to a set of sample data.

Interpretation

Binomial Distribution
The distributional parameter, the average proportion, is assumed for a given
population or is calculated by dividing the number of items in a sample that
meet the condition of interest (the count) by the total number of items in-
spected (the sample size). We can calculate the probability of counting x items
in a sample from a population with a known average proportion using Minitab
or MS Excel’s statistical function BINOMDIST.