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206 Part IV: Quality Assurance
Mean < Median < Mode
Left-skewed
Mean = Median = Mode
Symmetric
Mode < Median < Mean
Right-skewed
Figure 18.1
Frequency distributions showing the shape and location of measures
of centrality.
frequency. The data set is left-skewed when values in the data set that are greater
than the median occur with relatively higher frequency than those values that
are smaller than the median. The values smaller than the median are scattered
far from the median. Finally, the data set is right-skewed when values in the data
set that are smaller than the median occur with relatively higher frequency than
those values that are greater than the median. The values greater than the median
are scattered far from the median.
2. MEASURES OF DISPERSION
Calculate range, standard deviation, and
variance. (Application)
Part IV.A.2
Body of Knowledge IV.A.2
In the previous section we discussed measures of central tendency. As we saw
they provide us information about the location of the center of frequency distributions
of data sets under consideration. Information about variation is provided by
measures known as measures of dispersion. In this section we will study three measures
of dispersion including the range, variance, and standard deviation.
For example, consider the frequency distribution curves shown in Figure
18.2.
Measures of central tendency do not portray the whole picture of any data set.
For example, it can be seen in Figure 18.2; the two frequency distributions have
the same mean, median, and mode. Interestingly, however, the two distributions
are significantly different from each other. The major difference between the two
distributions is in the variation among the values associated with each distribution.
It is important then for us to know about the variation among the values
of the data set.