Engineering Anthropometry - Fundamentals and Assessment Tools for Occupational Ergonomics - page 180

175 188

162 Height in cm

2.5%

2.5% 95%

FIGURE 9.2 Frequency distribution of body height (stature) inAmericans. About 95%of all males are between 162 and
188 cm tall, about 2.5% are shorter, another 2.5% taller. (From Kroemer et al., Engineering Physiology. Bases of Human
Factors Ergonomics, 3rd ed., Van Nostraud Reinhold — John Wiley & Sons, New York, NY 1997. With permission.)

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male Americans; only 2.5% are shorter than approximately 1,620 mm, and another about 2.5% are taller
than 1,880 mm. In other words, about 95% of all men are in the height range of 1,620 to 1,880 mm,
because the 2.5th percentile value is at 1,620 mm and the 97.5th percentile is at 1,880 mm. The 50th
percentile is at 1,750 mm.
(In a normal data distribution, mean [m], average, median, and mode coincide with the 50th percen-
tile. The standard deviation [S] describes the peak or the flatness of the data set. More details on these
statistical descriptors are discussed later in this chapter under “Estimation by Probability Statistics.”)
There are two ways to determine the given percentile values. One is simply to take a distribution of
data, such as that shown in Figure 9.2, and to determine from the graph (measure, count, or estimate)
critical percentile values. This works whether the distribution is normal, skewed, binomial, or in any
other form. Fortunately, most anthropometric data are normally distributed, which allows the second,
even easier (and usually more exact) approach to calculate percentile values. This involves the standard
deviation, S. If the distribution is flat (the data are widely scattered), the value of S is larger than when the
data cluster is close to the mean.
To calculate the percentile value, one simply multiplies the standard deviation S by a factor k, selected
from Table 9.2. Then one adds the product to the mean m:

p ¼ m þ k S (9 : 1)

If the desired percentile is above the 50th percentile, the factor k has a positive sign and the product

k S is added to the mean; if the p-value is below average, k is negative and hence the product k S is

subtracted from the mean m.
Examples

1st percentile is at m þ k S with k ¼ 2 : 33 (see Table 9.2; note the negative value of k)

2nd percentile is at m þ k S with k ¼ 2 : 01

2.5th percentile is at m þ k S with k ¼ 1 : 96

5th percentile is at m þ k S with k ¼ 1 : 64

10th percentile is at m þ k S with k ¼ 1 : 28