I came across this in Runner's World magazine (Page 88, May, 2016). It seemed like a good application for a math class. It had the percentage of women in the field of the Boston Marathon. It seemed like it was something close to a linear relationship. Here is the data:
Year # Women # Men % of Women
1966 1 415 0.3%
1972 8 1,210 0.7%
1980 237 3,428 6.5%
1990 1,434 6,516 18.0%
2000 5,469 10,199 34.9%
2010 9,560 13,161 42.1%
2015 12,018 14,580 45.2%
I tried it out on an on-line calculator. First it is years vs. percentage of women. I used the point (0,0.3), (6,0.7), (14,6.5), etc.
The best fit was a linear equation of y = 1.0232x-3.8943. It had a correlation of 0.9866, so pretty good. I graphed it and perhaps some kind of logistic growth model perhaps some kind of logistics growth model might be a little better. The rate of increase of the percentages is starting to fall off a little.
I wasn't going to do this, but for fun I graphed years vs. number of women. It looked fairly parabolic. After plugging them in - (0,1,), (6,8), etc. I got the best fit to be:
y = 0.3888x^2.5833 with a correlation of 0.9751.
So, some interesting applications could be looked at from Algebra I through Advanced Math.
