Texas Mathematics Teacher Spring/Summer 2022 - 10

An Odyssey with Time Series: The Masters Golf Tournament
Second, the winning scores for 1940-1942 are all constant at 280 strokes, and this is indicated by the zero moving range
values for the seventh and eighth moving ranges, shown numerically in Table 3 and graphically in Figure 2. This chart
was quickly constructed using Microsoft EXCEL®
.
Individuals Chart Construction:
Similarly, an individuals chart provides a visual perspective on the long-term variation, or behavior, seen in a time series.
It is generally constructed as follows:
(a) Plot the actual time series measurements in a rectangular coordinate system where the horizontal axis denotes some
convenient time sequencing, and the vertical axis represents the measurements of interest.
(b) Plot a horizontal line through the Average (AVE).
(c) Plot a horizontal Upper Limit, UL, for individual measurements at UL = AVE + 2.66 * AMR.
(d) Plot a horizontal Lower Limit, LL, for individual measurements at LL = AVE - 2.66 * AMR.
The constant 2.66 is also an unbiasing constant, and it transforms the average moving range, by multiplication, into unbiased
lower and upper three-standard-deviation limits appropriate for the individuals chart.
Using the values in Table 2 and the average moving range of 2.0 strokes from above, compute (i) AVE = 282 strokes, (ii)
LL = AVE - (2.66 * AMR) = 282 - (2.66 x 2.0) = 276.7 strokes, and (iii) UL = AVE + (2.66 * AMR) = 282 + (2.66 x 2.0) = 287.3
strokes. Figure 3 shows the plotted results using all nine Pre-WWII time series values from Table 2. This chart was also
quickly constructed using Microsoft EXCEL®
.
Although the winning scores for 1939 through 1942 are somewhat lower than for the previous years, none of the points
plotted traverses the limits. So, we conclude that only routine variation in winning scores is present over the initial nine
years of The Masters tournament. Had any point crossed the limit lines, or had there been any bizarre (non-random) behavior
for points residing within the limits, then we would be justified seeking to learn why, if possible.
Figure 3. Individuals chart for Table 2 data
10 | Spring/Summer 2022
Texas Mathematics Teacher

Texas Mathematics Teacher Spring/Summer 2022

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