Who is Better?
How many times have you sat around and wondered about things like this?
Who is better
Kobe or Michael Jordan?
Tom Brady or Peyton Manning?
Barry Bonds or Jeter?
One Direction or 5 seconds of Summer?
We are going to use mathematics to justify your opinion.
In this project you are going to research someone that interests you, do a
cornucopia of math, and then prepare a presentation.
The Details
Part 1
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Pair up with someone that you like to argue with.
Choose an athlete, an artist, an author, musician, actor, etc...(any professional
in a field that interests you) NOTE: YOUR PERSON MUST HAVE BEEN
ACTIVE FOR AT LEAST 5 YEARS
You and your partner must choose a professional in the same field so that
you can compare statistics.
Go online and research one statistic for your person over the history of their
career. For example, if I chose to research Barry Sanders I could research
and collect data on how many rushing yards he ran for each season.
Collect your data in an input/output data table where X represents the years
active and y represents the total sum of your statistics for that year. Create
another input/output data table where X represents the years active and y
represents the statistic for each year. Remember you must obtain data for
that person’s entire career.
Example:
Barry Sanders rushing yards for five years are
Our research data should be collected like this
Year
1
2
3
Yards
1200
1300
1125
Total Yards 1200
2500
3625
4
885
4510
5
1025
5535
We should then create an input/output table for the cumulative data
Year
1
2
3
4
5
Total Yards
1200
2500
3625
4510
5535
We should also create an input/output table for the data year by year
Year
Yards
1
1200
2
1300
3
1125
4
885
5
1025
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Create two scatter plot graphs of the data that you collect (one for the total
cumulative statistic and one for the year by year statistic) on an X/Y
coordinate plane where x represents the years and y represents the your
statistic. Label and title your graph.
Determine if your data in each graph displays a linear relationship. If yes,
write an equation for the linear relationship. If no, explain why not.
Part 2
So far you have collected data and created a table to store the information and
created a scatterplot to represent your data visually. Now we are going to take the
data we collected and use mathematics to adjust the data to make it more user
friendly.
Your scatterplot more than likely did not represent a perfectly linear relationship.
We can use something called a line of best fit to “average” the data.
To create a line of best fit we must draw a straight line through your data points that
follows the trend of the points. Try to find a place to draw your line that is as close
to as many of your points as possible (as many data points above the line as you
have below the line). Do this for both of your graphs.
After you have drawn your line of best-fit answer the following questions about
each graph:
1. Is your line of best fit a good line of best fit? Are most of the points close to
your line? Explain your answer.
2. Do you have any outliers? (Outliers are points on your scatter plot that are
very different from the other points. These are the few random points that
are not close at all to your line of best fit).
3. Do you have any clusters? (Clusters are a group of points that are bunched
together on your scatter plot. These are relatively close to your line of best
fit.)
4. What is the slope of your line of best fit?
5. What is the y-intercept of your line of best fit?
6. Write an equation for your line of best fit.
7. Using your line of best-fit equation, what would your y value be if your
person were active for 10 additional years? Show your work.
Part 3
Now we are going to look at our data a different way.
1. Find the mean average for each of your input/output tables.
2. What does the mean average tell you about your data? Explain for what it
means for each of your tables.
3. How is the mean average useful? How do outliers affect your mean average?
4. Make a new input/output table for each data set using your mean averages
for your rate of change instead of the data that you actually found.
5. How does this change your data? Explain?
6. Graph the new average data on the same graph as your original scatterplots.
Use a colored pencil to show a different color for these graphs.
7. What is the slope of your new data? Interpret what the slope means in
context. (Do this for each of your new graphs)
8. What is the y-intercept of your new data? Interpret what the y-intercept
means in context. (Do this for each of your new graphs)
9. Write an equation in slope-intercept form for each of your new graphs.
10. Using your mean average equation, what would your y value be if your
person were active for 10 additional years? How does this compare to the yvalue you came up with in Part 2 number 7? Show your work.
11. Which graph more accurately shows your data, the line of best fit you created
or the mean average equation? Explain why?
Part 4
Debate time.
Take your data and choose either your line of best-fit equation or your meanaverage equation to compare your data to your partner’s data.
1. If both athletes played the same number of years who would have higher
statistics?
2. Create a short presentation using any software that you like using the data
you collected to prove why the person that you researched is better than the
person that your partner chose. Be creative and have fun. Your presentation
must use mathematics to justify your reasoning. You should include your
graphs, tables, equations, etc… in your presentation to support your
argument.