Progress of the World Record in the Mile Run

This activity has been adapted from an activity given in A sourcebook of Applications of School Mathematicsprepared by a Joint Committee of The Mathematical Association of America and the National Council of Teachers of Mathematics, 1980.

In 1875, Walter Slade of Great Britain ran a mile in 4 minutes, 24.5 seconds. At that time, it was the fastest anyone had ever been timed for the mile. Now, the fastest high school students do better. In 1993, Noureddine Morceli of Algeria set the current mile world record of 3 minutes, 44.39 second. Here is how the record has evolved in the years since 1875.

1875Walter Slade, Britain4:24.5

1880 Walter George, Britain4:23.2

1882George4:21.4

1882George4:19.4

1884George4:18.4

1894Fred Bacon, Scotland4:18.2

1895Bacan4:17.0

1911Thomas Connett, U. S.4:15.6

1911John Paul Jones, U. S.4:15.4

1913Jones4:14.6

1915Norman Taber, U. S.4:12.6

1923Paavo Nurmi, Finland4:10.4

1931Jules Ladoumegue, France4:09.2

1933Jack Lovelock, New Zealand4:07.6

1934Glenn Cunningham, U. S.4:06.8

1937Syndey Wooderson, Britain4:06.4

1942Gunder Haegg, Sweden4:06.2

1942Arne Andersson, Sweden4:06.2

1942Haegg4:04.6

1943Andersson4:02.6

1944Andersson4:01.6

1945Haegg4:01.4

1954Roger Bannister, Britain3:59.4

1954John Landry, Australia3:58.0

1957Derek Ibbotson, Britain3:57.2

1958Herb Elliott, Australia3:54.5

1962Peter Snell, New Zealand3:54.4

1964Snell3:54.1

1965Michel Jazy, France3:53.6

1966Jim Ryun, U. S.3:51.3

1967Ryun3:51.1

1975Filbert Bayi, Tanzania3:51.0

1975John Walker, New Zealand3:49.4

1981Sebasten Coe, Britain3:48.53

1981Steve Ovett, Britain3:48.40

1981Coe3:47.33

1985Steve Cram, Britain3:46.31

1993Noureddine Morceli, Algeria3:44.39

1999Hicham El Guerouj, Morocco3:43.13

Activities:

1.Enter the data into a graphing calculator and display the scatter plot.

Based on the data and the plot, guess an equation for a line which approximates the trend and

record your guess in the table below. Use the calculator to plot your guess. Then refine your

guess based on the how well the graph fits the data.

Equation
First Guess
Second Guess
Third Guess
Fourth Guess
Fifth Guess

(a)What does the slope of the equation signify?

(b)Use your equation to predict the mile world record in 2010.

(c)Use your equation to predict the year the mile world record may be 3:30.00.

(d)Are there limitations to your model? Explain.

(e)For the greatest difference between the actual and predicted time, find the year and amount.

2.Find the regression equations:

(a)Linear regression

(b)Exponential regression

(c)Logarithmic regression

(d)Quadratic, Cubic, or Quartic regression

(e)Some other regression equation

(f)Answer questions 1(b–e) for each regression equation.

(g)Are the results what you expected? Explain.

Other Activities:

Students could choose an event of their choice to investigate. Let students choose the distance, women/men, age group, or sport (track, swimming, etc.).

Women's times have been improving. Is the time gap between women's and men's times decreasing? Do the models predict a year when the women's and men's records will be the same?