Texas Mathematics Teacher Spring/Summer 2022 - 7

An Odyssey with Time Series: The Masters Golf Tournament
Stephen M. Scariano and Ananda B. W. Manage
This exposition serves as an introductory, time series data
exploration that can be pursued by those teaching upper
level (11th or 12th grade) high school students. With
careful instructor guidance, this scenario can be studied
by an entire class, or by teams of three of four students
each. The effort here is consistent with the Texas Essential
Knowledge and Skills for Mathematics (TEKS) guidance:
Title 19, Part 2, ยง111.47, sections b.3, c.2.B and c.2.E, as
well as the Guidelines for Assessment and Instruction in
Statistics Education (GAISE) Report: Framework Table
items I.B and II, sponsored by the American Statistical
Association.
Time series analysis is one of the most challenging
ventures facing modern data analysts. Discovering
the evolutionary features of an observable variable
as time marches on is as much art as it is science. The
effort typically begins with a time series plot, where the
horizontal is a time axis scaled in convenient units, while
the vertical axis corresponds to the measured values of a
variable of interest, also scaled appropriately. Of course,
a contextual background description is also essential
because real data only have meaning in context.
All sports provide a cornucopia of real-world data
amenable to time series analysis. Table 1 shows time
series data for The Masters golf tournament (https://www.
masters.com/en_US/tournament/past_winners.html) since
its inception in 1934, and published by Augusta National,
Inc. of Augusta, GA.
Each champion is listed by name and date alongside a
total score computed after playing four, complete 18-hole
golf games, which are called rounds.
Table 1 has a key feature common to many authentic data
sets: the tournament was not held during the critical years
1943-1945 of World War II (WWII), and such missing
data must be confronted and disclosed in any genuine
statistical analysis.
Most often, data are collected to answer one or more key
questions concerning the phenomenon that originally
created them. Cursorily scanning Table 1 seems to suggest
that champion scores may be decreasing over time. So, the
key question here is: Have the winning, four-round scores
for The Masters tournament champions been declining
over time, possibly indicating greater golfing expertise?
The techniques that follow will convincingly provide an
answer. Moreover, the statistical perspectives taken here
are easily accessible by secondary students.
Table 1. The Master's Champions since inception, along with Total Score after four rounds
www.tctmonline.org
Spring/Summer 2022 | 7
https://www.masters.com/en_US/tournament/past_winners.html https://www.masters.com/en_US/tournament/past_winners.html https://www.tctmonline.org/

Texas Mathematics Teacher Spring/Summer 2022

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