Title
Basketball Performance
Problem Statement
Suppose you are a
basketball player for your middle school. In the last 13 games you have
made the following number of baskets.
game #

# of baskets

1

4

2

7

3

7

4

3

5

8

6

3

7

5

8

3

9

4

10

5

11

7

12

6

13

7


Based on your performance in the first 13 games, how
many baskets do you think you will make in game 14? Explain your answer.
Problem setup
If a middle school student
scores points in a series of 13 basketball games as shown
in this table, what can we determine about how many points he will score in
game 14.
Plans to
Solve/Investigate the Problem
Using measures of central
tendency (range, mean, mode, median), I planned to investigate the
statistics and determine from them if there was a relationship or trend
within the figures. I also
decided to plot a graph using the game numbers as ‘x’ values
and the number of points as ‘y’ values.
Investigation/Exploration
of the Problem
Extensions of the Problem
After calculating the range (5), the mean
(5.3), the mode (7), and the median (5), I determined that there wasn’t
really enough information to find a trend or pattern. I then graphed the figures as
mentioned above on a scatter plot using the TI 83 calculator
and still could not see any correlation. Using statistical functions on the
calculator, I developed a line of best fit for the given statistics. The line was almost completely
horizontal and not very helpful.
At this point, I referred back to the
scatter plot and saw that if I were to disregard the first three games,
there was a gradual upward trend with limited exception (game 5). I then plotted the graph using the
last 10 figure and disregarding the first three. The line of best fit had a much more
positive slope. The mindset is
that possibly the basketball player was not shooting the ball properly
until just prior to the fourth week, and then he began to make systematic
improvement.
Author & Contact
Kevin Smith
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