# 100 Meter Freestyle

## Freestyle Swimming

Freestyle is a type of swimming competition where swimmers have limited restrictions on their stroke. Freestyle races are the most common of all swimming styles with distances up to 1500m or 1650 yards. The stroke most commonly used in freestyle races is the front crawl because it is generally the fastest. The 100 meters freestyle is the considered to be the highlight of the sport of swimming. The current men's world record holder is César Cielo Filho and the current women's world record is held by Britta Steffen. Both set their record during the 2009 World Aquatics Championships.

## The Goal of the Study

In many olympic events women’s performance is getting closer to the same level as men’s. Even though men may have better times than women, the women are improving more in some events by increasing at a faster rate. But in some events men and women are both slowing down. We are trying to determine if women’s performance is likely to surpass men’s performance for a certain event and when that will happen.

1. First we used winning results to make a table in our graphing calculator to display men's and women's performance for the event we chose.
2. Then we made a scatter plot for our data.
3. Next we created a line of best fit for each set of data.
4. Then we found the equation for each of our lines of best fit.
5. Finally using the equations for the lines of best fit we solved the system of equations.

## The Scatter Plot

The black squares represent male competitors. The blue squares represent female competitors.

## The Linear Regression (Lines of Best Fit)

Each line represents the trend for the male and female Olympic Gold Medalist times. The red represents the female trend line and blue represents the male. The equation for the female trend line is y = -0.075x + 203.609. The equation for the male trend line is y = -0.082x + 211.863.

## Intersection

Currently men are performing better at 100 meter freestyle than women in Olympic competitions because their times are faster. But both of their times are decreasing at about the same rate. Based on a linear regression, it is predicted that women and men won't ever have the same times and in the future women will never surpass men. From the graph we can see that the intersection point was somewhere even before the Olympics started. Since the intersection was such a long time ago we can't expect women and men's times to be the same. Also since the slopes of the lines are so close it is predicted that women won't surpass men in this event. Even if the times keep decreasing the men’s gold medalist time should still be faster than the women’s gold medalist time.

## X Coordinate

The x coordinate was the year in which men and women's times for this event would be the same. For this data the intersection was a year even before the olympics started. I couldn't find an exact coordinate because that would take a lot of scrolling. This means that if the Olympics had started before the year or in the year of the x value in the intersection that would have been when the men and women would have had the same times for this event.

## Y Coordinate

The y coordinate was the time that both the men and women would have in common for their gold medalists. For this data the intersection was a year even before the Olympics started. I couldn't find the the exact coordinate but it would most likely have a y value that is much greater than some of the times for this event now. This means that if the Olympics had started a very long time ago the intersection would have a y value of the time that both men's and women's gold medalists have in common.