Intermath | Workshop Support

 Write-up

Title

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
Email me!