The following are 13 world record times for men and women in the mile race as ratified by the International Association of Athletics Federations. The mile is the only non-metric distance that is recognized for record purposes. The times are given in minutes and seconds. Notice times prior to 1981 are accurate to a tenth of a second. Beginning in 1981, IAAF began recognizing times to a hundredth of a second. Also notice that the years of the records a
The following are 13 world record times for men and women in the mile race as ratified by the International Association of Athletics Federations. The mile is the only non-metric distance that is recognized for record purposes. The times are given in minutes and seconds. Notice times prior to 1981 are accurate to a tenth of a second. Beginning in 1981, IAAF began recognizing times to a hundredth of a second. Also notice that the years of the records are not the same for men and women. (Data from Wikipedia.org/wiki/mile_run_world_record_progression)
|
Year |
Men's Times |
Times in Seconds |
Athlete's Nationality |
|
1965 |
3:53.6 |
|
France |
|
1966 |
3:51.3 |
|
US |
|
1967 |
3:51.1 |
|
US |
|
1975 |
3:51.0 |
|
Tanzania |
|
1975 |
3:49.4 |
|
New Zealand |
|
1979 |
3:49.0 |
|
UK |
|
1980 |
3:48.8 |
|
UK |
|
1981 |
3:48.53 |
|
UK |
|
1981 |
3:48.40 |
|
UK |
|
1981 |
3:47.33 |
|
UK |
|
1985 |
3:46.32 |
|
UK |
|
1993 |
3:44.39 |
|
Algeria |
|
1999 |
3:43.13 |
|
Morocco
|
|
Year |
Women's Times |
Times in Seconds |
Athlete's Nationality |
|
1967 |
4:37.0 |
|
UK |
|
1969 |
4:36.8 |
|
Netherlands |
|
1971 |
4:35.3 |
|
West Germany |
|
1973 |
4:29.5 |
|
Italy |
|
1977 |
4:23.8 |
|
Romania |
|
1979 |
4:22.09 |
|
Romania |
|
1980 |
4:21.68 |
|
US |
|
1981 |
4:20.89 |
|
Soviet Union |
|
1982 |
4:18.08 |
|
US |
|
1982 |
4:17.44 |
|
Romania |
|
1985 |
4:16.71 |
|
US |
|
1989 |
4:15.61 |
|
Romania |
|
1996 |
4:12.56 |
|
Russia |
The purpose of this project is for you to apply concepts we have discussed in class, such as modeling with the TI-83/84 calculator, drawing scatter plots, making predictions, and solving systems of linear equations. The process you are to use is outlined below. Once you have completed the project, you should upload a neatly written
Using the Desmos graphing calculator or graph paper (which may be printed from an online image), complete the following steps:
- Visualize the data
- Use the horizontal axis (x) to represent the year. Begin with year 1960 and continue through year 2050. Choose an appropriate scale for the x-axis to model the data.
- Convert all the times to unrounded seconds instead of minutes and seconds; list these times in the table under “Times in Seconds.”
- Use the vertical axis (y) to represent the times, in seconds. Begin with 200 seconds and continue to 300 seconds. Choose an appropriate scale for the y-axis to model the data.
- Use an “x” to represent the data for men and plot the points on the grid using the year as the x-coordinate and the times for men as the y-coordinate. Use an “o” to represent the data for women and plot the points on the same grid using the year as the x-coordinate and the times for women as the y-coordinate.
- e) Title your graph and label the x and y Insert your graph below.
- Find the models
- Using the years as x and the times in seconds for men as y, enter the mens’ data in your calculator in L1 and L2, respectively. Do the same for women, except use L3 and L4 . Set up the plots in your calculator to display L1 and L2 as Plot1. Set up Plot2 to display L3 and L4. [Recall that the setup for plots is done with 2nd, Y=. Make sure that each plot uses a different mark so that you can distinguish between the two.] Use Zoom 9 to view the
scatter plot once you have set up the plots. Then adjust the window to match the grid on your graph paper and insert a picture of your calculator graph below. It should resemble the one you created by hand.
- Using the Calculate menu under Stats, find a linear regression model for L1 and L2. Write the corresponding equation, rounding to three decimal places for a and b.
- Using the Calculate menu under Stats, find a linear regression model for L3 and L4. Note that the format will be LinReg (y=ax+b) (L3,L4). Write the corresponding equation, rounding to three decimal places for a and b.
- d) Draw the two lines whose equations you found in parts b) and c) on the
graph you produced in part 1. Where do the lines appear to intersect? Give approximate coordinates, based on the grid, as integers.
Note:
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