MAT 243 Project One Summary Report Template
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School
Southern New Hampshire University *
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Course
243
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Mathematics
Date
Apr 3, 2024
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docx
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MAT 243 Project One Summary Report
Canyon Jessee
canyon.jessee@snhu.edu
Southern New Hampshire University
1.
Introduction: Problem Statement
We are trying to compare the Warriors of 2013-2015 to the 1996-1998 Bulls. They played two totally
different styles of basketball, so we want to see which style of play is more statistically benficial. We are going to be creating tables and graphs to show the data. This will have assigned confidence levels to show how confident we are in the data we have analyzed.
2.
Introduction: Your Team and the Assigned Team
Table 1. Information on the Teams
Name of Team
Assigned Years
1. Yours
Warriors
2013 - 2015
2. Assigned
Bulls
1996-1998
3.
Data Visualization: Points Scored by Your Team
We will be using a histogram to show the data of our team. We are using it to show the distribution of the points scored per game. This plot is almost normally distributed but has some a surge in the middle and a dip on the high end. Overall they seem to have scored over 100 points per game in over half of their games during this time. 4.
Data Visualization: Points Scored by the Assigned Team
We will be using a histogram for the Bulls as well, since it will allow for easier comparison visually. This team was also a fairly normal distribution and seems to be more clustered in the middle and not as many range of outcomes. This could mean that they were more consistant in their points.This
range of outcomes being limited also made the middle of the graph peak at a few points.
5.
Data Visualization: Comparing the Two Teams
Since we used histograms to show the data, to compare them we will also be using an overlayed histogram. This will allow us to compare the data we just went over. In the comparison, you can see that
the Warriors distribution seems shifted slightly more to the right. They also have a higher high and a higher low end, this means that they were regularly scoring more points than the Bulls during this time. 6.
Descriptive Statistics: Points Scored By Your Team in Home Games
Table 2. Descriptive Statistics for Points Scored by Your Team in Home Games
Statistic Name
Value
Mean
106.62
Median
106.0
Variance
136.76
Standard Deviation
11.69
Central Tendancy and variability are use to show what we can expect from our team. The mean is on average how much can we expect the Warriors to show. The mean is the absolute middle of all of our collected data, and is very close to the mean in this case. The variance is used to see how far the data is spread out from the mean the entire set of data is, since our data is spread by 60 points, this was expected to be fairly high. And the standard deviation is used show how far from the mean a single piece of data is. There is a range of about 12 points that would be normal on any given night as that is where a lot of the data is. There will be outliers due to how high the variance is. Both of the mean and median are really close in this data set, so there is not really much of a reason to chose one over the other. In general we would use mean to get the answer especially if we are using variance to see how different certain games
are from one another. The data itself is fairly bell-shaped in general.
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7.
Descriptive Statistics: Points Scored By Your Team in Away Games
Table 3. Descriptive Statistics for Points Scored by Your Team in Away Games
Statistic Name
Value
Mean
103.63
Median
104.0
Variance
130.77
Standard Deviation
11.44
This data is close to our home game data but it does differ a bit. For one, using the mean we can see that
the average number of points is down from about 107 to 104. The standard deviation is also slightly lower than the home games, althought it is very slightly. This means that the Warriors seem to stuggle slightly more in away games versus home games on a consistant bases. This data would also be bell shaped 8.
Confidence Intervals for the Average Relative Skill of All Teams in Your Team’s Years
Confidence Level (%)
Confidence Interval
95%
(1502.02, 1507.18)
We are 95% confidence that the relative skill of the league was from 1502.02 to 1507.18. This is the average relative skill of the league, we use the 95% to give us a good guess at it. If we were to raise the confidence to a higher level, it would make the interval a little larger to give us more room for the data to fall in there. There is a 81% chance that any given chance that a team has less skill than than these Warriors during this time frame. Based off what we saw them do in the league, this makes sense since they were really good during that time. Statistically it shows how strong of a team they were compared to other teams.
9.
Confidence Intervals for the Average Relative Skill of All Teams in the Assigned Team’s Years
Table 5. Confidence Interval for Average Relative Skill of Teams in Assigned Team’s Years
Confidence Level (%)
Confidence Interval
95%
(1487.66, 1493.65)
We are 95% confidence that the relative skill of the league was from 1487.66 to 1493.65 during the years 1996 to 1998. If we were to lower the confidence level, it would make the interval smaller but make it have a lot more of a chance to be wrong. So this data shows that the league was weaker during 1996-1998 than it was in 2013-2016. The Bulls had a 97% chance that any given team had less skill than them which is a crazy level of domination.
10. Conclusion
We used graphs to make the data easier to visualizing. Seeing how dominant each of these teams were and being able to compare them could help us find out what worked for each team. Using this data we can see that the the Bulls were even more dominant than the Warriors were, but it was a weaker era of NBA basketball.