STATISTICAL TECHNIQUES IN SOFTWARE SIX SIGMA AND DESIGN FOR SIX SIGMA (DFSS) - Software Design for Six-Sigma: A Roadmap for Excellence - page 132

6.3.1.1 Measures of Central Tendency. Measures of central tendency are
measures of the location of the middle or the center of a distribution of a functional
requirement variable (denoted as y ). The mean is the most commonly used measure
of central tendency. The arithmetic mean is what is commonly called the average.
The mean is the sum of all the observation divided by the number of observations in
a sample or in a population:
The mean of a population is expressed mathematically as:

i = 1 y i
N

N

µ y =

where N is the number of population observations.
The average of a sample is expressed mathematically as:

i = 1 y i
n

n

y =

where n is the sample size.
The mean is a good measure of central tendency for roughly symmetric distribu-
tions but can be misleading in skewed distributions because it can be influenced greatly
by extreme observations. Therefore, other statistics such as the median and mode may
be more informative for skewed distributions. The mean, median, and mode are equal
in symmetric distributions. The mean is higher than the median in positively skewed
distributions and lower than the median in negatively skewed distributions.
The median is the middle of a distribution where half the scores are above the
median and half are below the median. The median is less sensitive to extreme scores
than the mean, and this makes it a better measure than the mean for highly skewed
distributions.
The mode is the most frequently occurring score in a distribution. The advantage
of the mode as a measure of central tendency is that it has an obvious meaning.
Furthermore, it is the only measure of central tendency that can be used with nominal
data (it is not computed). The mode is greatly subject to sample fluctuation and is,
therefore, not recommended to be used as the only measure of central tendency.
Another disadvantage of the mode is that many distributions have more than one
mode. These distributions are called “multimodal.” Figure 6.5 illustrates the mean,
median, and mode in symmetric and skewed distributions.

6.3.1.2 y ) disper-

sion is the degree to which scores on the FR variable differ from each other. “Variabil-
ity” and “spread” are synonyms for dispersion. There are many measures of spread.
The range ( R ) is the simplest measure of dispersion. It is equal to the difference
between the largest and the smallest values. The range can be a useful measure of

Measures of Dispersion. A functional requirement (FR =