9/12/11

The U.S. Open• This table shows

country of origin for each of the men’s singles champions from 1970 to 2010. The U.S. winners are highlighted in red.

The U.S. Open• Let’s change this to

numerical data by assigning a U.S. winner to1 and a non-U.S. winner to -1. This is the revised table.

The U.S. Open• Create a bar graph

of the data in the table.

• You’ll see that there seems to be a periodic trend in the data for U.S. winner.

The U.S. Open• Let’s smooth out the

data this way:– If a U.S. winner is not

part of a group of 2 or more, assign its value to -1.

• Here is the revised graph. Now you can see the periodic nature of the U.S. winning streaks.

The U.S. Open• We can overlay a

sinusoidal curve over this graph to more clearly see the periodic nature of the data set.

• Notice that these sinusoidal curves have different widths.

The U.S. Open• The period of the

first sine curve is 15 years. The period of the second curve is 12 years. And the period of the third curve is 9 years.

• The average period is 12 years.

The U.S. Open• We can now

construct a periodic model from the data set.

• A standard sine function has a period of 2π.

The U.S. Open• To change the period

to 1, multiply the x by 2π.

• This function can be used as the basis for creating a function of period 12, representing the average cycle for U.S. dominance in tennis at the U.S. Open.

The U.S. Open• This function has a

period of 12.• We now just need to

adjust it so that it is in sync with the periodic nature of our data set.

The U.S. Open• This is the function

that models the data set, and according to the graph, the U.S. will once again have dominance at the U.S. Open around 2016, and then once again in 2028.

The U.S. Open• Buy why would

American dominance at the U.S. Open be periodic?

• When there is a dominant player (or players) they have a much higher probability of winning and during their prime, they will have several championships.

The U.S. Open• Here is the graph

again, this time with actual winners identified.

Jimmy ConnorsJohn McEnroe

Andre AgassiPete Sampras

Andy RoddickPete Sampras

The U.S. Open• If the trend holds up,

then there is likely to be one or more American players who will become dominant over the next few years.

Jimmy ConnorsJohn McEnroe

Andre AgassiPete Sampras

Andy RoddickPete Sampras

The U.S. Open• As a final activity,

here is the data for the women’s singles champions over the same period. Perform the same kind of analysis we did with the men’s data. What can you conclude?