Texas Mathematics Teacher Spring/Summer 2022 - 11

An Odyssey with Time Series: The Masters Golf Tournament
Table 1 Data Analyzed by Stage
Figure 4. Center lines, and lower and upper limits by stage for all years
Figure 4 shows champion scores for all the years in Table 1, separated into stages. A stage is a time period when the process
appears to be stable in its average level and its variation around that level. The purpose of studying the stages of a
time series is to gain insight, if possible, into their causes. Each stage has its own center line, and lower and upper limits
used to judge differences between exceptional (plotting beyond limits) behavior and routine (plotting within limits) behavior.
Choices for the number of stages as well as the stage lengths are not unique, but they should be constructed with
the intent of identifying periods of relative stability, if any. Figure 4 was quickly constructed using Minitab 17®
commercially available software products offer staging options for time series behavior charts.
, but many
Table 4a gives the computed center lines and limits appearing in Figure 4, while Table 4b provides the averages and standard
deviations for the data stream by stage.
Table 4a. Center line and limits by stage
Table 4b. Average and standard deviation by stage
What can be gained from Figure 4 over Figure 1? The answer is statistical quantification. Table 4a shows the overall level
and variation around that level for each stage, and we can visually separate exceptional variation from routine variation.
The moving range chart for Stage 1 shows the most consistency (in variation) of all stages, even though that consistency
is coupled with the highest average score over all stages. Scanning down the third column of Table 4b shows that the
standard deviation of scores in Stage 1 is roughly 44% (1.77/4) of the standard deviations seen in Stages 3 and 4, even as
column 1 of that table shows that the average scores have decreased from a high of 282 strokes to a low of roughly 277
strokes. Practically speaking, this accounts for roughly a 282 - 277 = 5 stoke decrease over the life of The Masters tournament.
So, there is no doubt that Masters champion scores have decreased over time by about five strokes, while it appears
that the standard deviation of winning scores since WWII is roughly consistent at 4 ≈ (4.14 + 4.06)/2 strokes.
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Texas Mathematics Teacher Spring/Summer 2022

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