Page 242 - Applied statistics and probability for engineers

220 Chapter 6/Descriptive Statistics

Sometimes it can be very helpful to combine a time series plot with some of the other
graphical displays that we have considered previously. J. Stuart Hunter (The American Statis-
tician, 1988, Vol. 42, p. 54) has suggested combining the stem-and-leaf plot with a time series
plot to form a digidot plot.
Figure 6-17 is a digidot plot for the observations on compressive strength from Table
6-2, assuming that these observations are recorded in the order in which they occurred.
This plot effectively displays the overall variability in the compressive strength data
and simultaneously shows the variability in these measurements over time. The general
impression is that compressive strength varies around the mean value of 162.66, and no
strong obvious pattern occurs in this variability over time.
The digidot plot in Fig. 6-18 tells a different story. This plot summarizes 30 observations on
concentration of the output product from a chemical process where the observations are recorded
at one-hour time intervals. This plot indicates that during the irst 20 hours of operation, this
process produced concentrations generally above 85 grams per liter, but that following sample
20, something may have occurred in the process that resulted in lower concentrations. If this vari-
ability in output product concentration can be reduced, operation of this process can be improved.
Notice that this apparent change in the process output is not seen in the stem-and-leaf portion of
the digidot plot. The stem-and-leaf plot compresses the time dimension out of the data. This illus-
trates why it is always important to construct a time series plot for time-oriented data.

Sales, x Sales, x

19821983 1984 1985 1986 19871988 1989 1990 1991 Years 1 2 3 4 1 2 3 4 1 2 3 4 Quarters
1989 1990 1991
(a) (b)
FIGURE 6-16 Company sales by year ( )a . By quarter ( )b .

Leaf Stem Time series plot

5 24
7 23
189 22
8 21
7108 20
960934 19
0361410 18
8544162106 17
3073050879 16
471340886808 15
29583169 14
413535 13
103 12
580 11
15 10
FIGURE 6-17 A 7 9
digidot plot of the 7 8
compressive strength 6 7
data in Table 6-2.