CFrench - MAT 243 Project One Summary Report
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Southern New Hampshire University *
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243
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Mathematics
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Apr 3, 2024
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MAT 243 Project One Summary Report
Christian French
christian.french@snhu.edu
Southern New Hampshire University
1.
Introduction: Problem Statement
The reason for this report is to analyze the historical data for basketball teams and find and analyze performance patterns, as well as distributions of key performances. This analyzation is set to aid the management in making improvements to their team. The two data
sets I will be analyzing is the Nuggets from 2013 to 2015, and the Bulls from 1996 to 1998. Both of whom will have their own unique data charts, averages, and confidence intervals. I will be using data visualization and confidence intervals to calculate the average skill of both teams in their respective years.
2.
Introduction: Your Team and the Assigned Team
The team I was chose was the Nuggets, years 2013-2015, and the team assigned to me by management was the Bulls, years 1996-1998.
Table 1. Information on the Teams
Name of Team
Assigned Years
1. Yours
Team Nuggets
2013- 2015
2. Assigned
Team Bulls
1996-1998
3.
Data Visualization: Points Scored by Your Team
Data visualization is used to study data distributions and trends by giving us a visual way to not only understand, but also see trends, outliers, and patterns within the data that is presented. Data visualization puts all of this into an image that is more easil digestible and understandable.
When it comes to the visualization for points scored by my team, the Nuggets, from 2013
to 2015, I chose the bar graph over the scatter plot. The goal of this visualization is to accurately show the information presented on the graph. With the scatterplot, the points are lined in three spots, with two extra years added on to each side, making the dots clustered and hard to read. Between around 90-120, the points are clustered to the point where its hard to tell the exact number of points chosen. The coach wanted a distribution, and I believe the
bar graph shows that with a precision that is needed. The bar graph showcases the number of points received and how often they had them, giving him a better idea of how they perform as a whole over the course of three years instead of struggling to see an average or the exact numbers in the scatter plot. For instance, they scored 100 points most often, with scoring 100
points with a frequency of 35, and had an average of 110 and 115 points with a frequency of 30. This is able to show the visualization of their averages and how often they perform on a better level.
4.
Data Visualization: Points Scored by the Assigned Team
I chose the same graph for the Bulls for the same reason. Being able to see the same charts with comparative data is the best way to showcase the average of both teams and showcase how they compare. For instance, the Bulls scored 105 points with a frequency of 35, and when comparing the two, you can see their highest frequency has a difference.
5.
Data Visualization: Comparing the Two Teams
For the comparison of the two teams, I chose the box plot because I feel like it’s a better comparative than the histogram is. The histogram overlays the two and, due to the fact that on around one half of the graph the Nuggets are performing better and the Bulls perform better on the other half and it can cause confusion over who truly performs better. With the boxplot, there is a clear distinction between the two teams where you can see that the Nuggets performed better, even if it was by a small margin. With the boxplot, you can see the three outliers the Nuggets have, two being over 135 mark, and one under the 70 mark, while the Bulls have no outliers. On top of that, you can see the three point average between the variance and mean of their overall points. With the boxplot, you are able to more clearly see the difference while having all of the information about the two teams’ performances presented clearly.
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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
106.2
Median
106
Variance
147.8
Standard Deviation
12.16
There was a further delve into the Nuggets, seeing how well they perform when in comparison to home games and away games. When it came to home games, the central tendency was a mean of 106.2 points scored and a median of 106 points. Given that there is only a .2 difference between the two values, it means that the data is symmetrical and is considered normal. This would form a bell shaped graph, with the tiniest hint of a right skew as the median is .2 higher than the mean. The median is the best option to represent the center of the distribution as this dsistribution has outliers, and the median is uneffected by them. Looking at the variability, there lies a variance of 147.8 and a standard deviation of 12.16. This variance of 147.8 means that there is a wide array of values and they are not clustered around the mean. This
means that there is a spread of how many points the Nuggets score at home games and their performance can vary widely between games. The standard deviation shows that there is, on average, a 12.16 point variance from the mean, so taking that into account, there is a noticeable average of how many points they score, even if they have some extreme highs or lows on occurrence with different games.
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
101.8
Median
103
Variance
148.33
Standard Deviation
12.18
When it comes to their away games, they have a mean of 101.8 and a median of 103. Like with the home games, there is not a high variance or skew when it comes to the number of points scored each game. It suggests that these values are roughly centered around these two points. With a variance of 148.33 and a deviation of 12.18, there is also a noticeable variation between my points, all that still remains normal. However, considering the mean and median are just a couple points less, and the variance and standard deviation almost the same, the variance will be higher, even if its not by that much. When comparing the two, all values are similar. This will have the same slight skew to the right, as the variables are close together in both plots. This shows that there is a tight correlation on how they play all their games, whether it be home or away, and how there is some consistency each performance. However, based off of the two tables, the Nuggets are playing better at home games, even if its by a 5 point higher average.
8.
Confidence Intervals for the Average Relative Skill of All Teams in Your Team’s Years
Table 4. Confidence Interval for Average Relative Skill of Teams in Your Team’s Years
Confidence Level (%)
Confidence Interval
95%
(1502.02, 1507.18)
Confidence intervals are generally used in estimating the measures of central tendency for a. population giving us a parameter and indicting to us the reliability of that estimate, while also acknowledging the uncertainty that comes with it. For instance, with this confidence interval, it is implied that we are 95% positive that the average relative skill of all teams (all the samples) means from 2013-2015 falls within the range of 1502.02 and 1507.18. 95% is the standard as it gives leeway for error (uncertainty) and the confidence level isn’t so high you have a range that is too big. If the interval were different, such as being 99%, the range would have been wider. When it comes to higher confidence intervals, we would have a higher confidence in the range that is given, but it comes at the price of a higher range, meaning there is a wider range on where these scores will fall. The probability that a given team in the league has a relative skill lower than the Nuggets is 0.5786, or 58%. Given that the percentage is so high, I would say that it is not unusual. With a higher percentage, it is assumed that it is a more common occurrence, rather than being something that happens once in a while. If the percentage was lower, then it would be unusual. 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)
The Bulls with a confidence interval of 95%, it is implied that we are 95% positive that the average relative skill of all teams (all the samples) means from 1996-1998 falls within the range of 1487.66 and 1493.65. If the interval were different, such as being 99%, the range would have been wider. When it comes to higher confidence intervals, we would have higher
confidence in the range that is given, but it comes at the price of a wider range, meaning there is a wider range on where these scores will fall. When taking into account the confidence intervals of both teams, comparing the higher range of the Nuggets compared to the slightly lower one of the Bulls, it can be seen that The Nuggets have a better overall assessment and a higher relative skill, respective to both sets of years. 10. Conclusion
The importance of the analysis that was performed, we were able to identify patterns, find
the central tendency and variability, and find a correlation. In finding these, we were able to accurately compare and contrast both the Bulls and the Nuggets and see the skill levels in both in order to understand improvement that has been made within the league and see the overall comparison of the Nuggets to present and past teams. Furthermore, this analysis provided us with the necessary information to move forward. The 1996-1998 scores for the Bulls had a lower standard deviation, mean, median, and variation than the Nuggets. This proves that the Nuggets had an overall higher score in performance and skill. Considering this, the team managers will know how to update their improvement and keep their team accurate and on top.
11. Citations
zyBooks, a Wiley brand. (2019). Linear Algebra. https://www.zybooks.com/catalog/applied-
statistics-with-data-analytics-python/ (accessed 2024).
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