4 X 100M Medley Relay

Swoosh and Woosh

What is it?

Medley relay swimming is when four swimmers swim a combination of four different swimming styles. These are freestyle, breaststroke, backstroke, and butterfly. This competition requires stamina, and this completion is part of the summer olympics. This event started in 1960 and continues to this day.
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An Unlikely Match

I wanted to compare the men and women timings for this event even though men and women do not compete against each other in the olympics. I did this by comparing all of the data and then matching it up with systems of linear equations.

The Goal of the Study

My goal was to use systems of linear equations and mathematical reasoning to analyze the trends of either gender in the 4 by 100 meter medley relay event. I also wanted to know which gender would outperform the other gender in the future, and when this would happen. This is my goal for this study.

The Data

This event started in 1960. The first column is the years. The second column is the men, and the last column is the women.

The Scatter Plot

The blue open squares represent the male points. The magenta Xs represent the female times.

The Linear Regression

Each line represents for the male and female olympic gold medalist times. Red represents the female trend line, and the blue represents the male trend line.

At the Crossroads

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The intersection point of these to lines is a very important thing to know. It shows for what x value or y value the lines meet at. When seeing the data above, it is evident that both men and women competitors are getting faster over the years. It can be concluded this way because as the years go on (x coordinate), the time (y coordinate) continues to decrease. It can also be seen that the women competitors have decreased their timings at a faster rate compared to the men. This can be seen, because the red line has a smaller slope. Currently, the men are outperforming the women; however, after the intersection point the women will start to outperform the men.


The independent variable are years the event was competed in. According to the data, at approximately year 2104. This is an olympic year. This is the year when both the men and women have equivalent timings. From then on, the women will outperform the men.


The dependent variable is approximately 145.56 seconds. This round to approximately 2 minutes and 26 seconds. This is the approximate gold medalist time for both men and women if the event was held in year 2104. From that point on the women are predicted to have faster times.
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