vdoc

Chapter 18: A. Basic Statistics and Applications 207
Mean = Median = Mode
Figure 18.2 Two frequency distribution curves with equal mean, median, and mode values.
Range
The range of a data set is the easiest measure of dispersion to calculate. Range is
defined as follows:
Range = Largest value – Smallest value (18.4)
Range is very sensitive to the influence of outliers and is not a very efficient
measure of dispersion since it takes into consideration only the largest and the
smallest values and does not take any account of the remaining observations. For
example, if a data set has 100 distinct observations, it uses only two observations
and ignores the remaining 98 observations. As a rule of thumb, if a data set contains
less than 10 observations, the range is considered as a reasonably good measure
of dispersion. Otherwise the range is not considered to be a very efficient
measure of dispersion.
EXAMPLE 18.9
The following data give the tensile strength (in psi) of a material sample submitted for
inspection:
Part IV.A.2
Find the range for this data set.
8538.24, 8450.16, 8494.27, 8317.34, 8443.99,
8368.04, 8368.94, 8424.41, 8427.34, 8517.64
Solution:
The largest and the smallest values in the data set are 8538.24 and 8317.34 respectively.
Therefore, the range for this data set is:
Range = 8538.24 – 8317.34 = 220.90