MAT 243 Project One Summary Report (2)
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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
Patrick Brizuela
Patrick.brizuela@snhu.edu
Southern New Hampshire University
1.
Introduction: Problem Statement
This report was conducted to analyze data gathered from the NBA historical data bank. The problem that I will be attempting to solve using the gathered data is to assist the head coach and front office management make decisions to further improve the team’s future performance. The data variables used to analyze performance patterns include points scored, relative skill level, years played, and if it was a home or away game. The statistical methods used in this analysis are data visualization, confidence intervals, and descriptive statistics (mean, median, variance, and standard deviation).
2.
Introduction: Your Team and the Assigned Team
For this analysis project, I was assigned the Chicago Bulls from the 1996-1998 seasons and I selected my childhood team, the Los Angeles Lakers during the 2013-2015 seasons.
Table 1. Information on the Teams
Name of Team
Assigned Years
1. My Team
Los Angeles Lakers
2013-2015
2. Assigned
Chicago Bulls
1996-1998
3.
Data Visualization: Points Scored by Your Team
Data visualization is used to study data distributions and trends by representing the data in a visual and graphic way. This is a simple way to see trends, growth, and changes with a large data element. There are many variations to be able to visualize information in the form of graphs, maps, and charts. In this project, there were a few types of data visualizations that were produced (histogram, scatterplot, and boxplot). As shown above, I chose to illustrate the
points scored by the Los Angeles Lakers during the 2013-2015 seasons using a histogram. Histograms represent the distribution of a continuous variable. This is accomplished by dividing into bins and counting the number of observations in each bin. When it comes to a single variable for viewing purposes, a histogram is best to use. 4.
Data Visualization: Points Scored by the Assigned Team
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For this, I chose the histogram again because it was the best visual representation of data being observed on a continuous variable. This histogram shows that it almost has a bell-like shape to the curve of the data, which leads me to believe that the mean, mode, and median are close to the same.
5.
Data Visualization: Comparing the Two Teams
For this, I preferred the overlapping histogram over the boxplot because it really helped to compare the differences as well as the similarities in the two data sets between the Los Angeles Lakers and the Chicago Bulls. With the overlap, you can really see the data comparison very easily. 6.
Descriptive Statistics: Points Scored By Your Team in Home Games
The measurement of the central tendency refers to the mean, median, and mode. These indicate the central location of a distribution. Whereas variance and standard deviation are representative of variability. Statistics allows us to compare how one data set varies from another. Our mean is 101.70, with the calculations done by adding all the scores and dividing by the total population. The mid-value score of the Lakers would be calculated by the median of 102.00. Variance is 149.18 which represents the average square difference from the mean and
the standard deviation of 12.21, or the square root of our variance. With the median slightly higher than the mean, which means that the data set for home games would be skewed to the left.
Table 2. Descriptive Statistics for Points Scored by Your Team in Home Games
Statistic Name
Value
Mean
101.70
Median
102.00
Variance
149.18
Standard Deviation
12.21
7.
Descriptive Statistics: Points Scored By Your Team in Away Games
The mean for the Lakers on away games was 100.71, where the median was 101.00, variance was 88.16, and a standard deviation of 9.39. The median slightly higher than the
mean, tells us that the data set would be slightly skewed to the left as well for away games. Central tendency would be best seen to the left of the median and provide the central distribution. The performance by the Lakers is similar playing both home and away games with a slight increase of at least three more points at home.
Table 3. Descriptive Statistics for Points Scored by Your Team in Away Games
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Statistic Name
Value
Mean
100.71
Median
101.00
Variance
88.16
Standard Deviation
9.39
8.
Confidence Intervals for the Average Relative Skill of All Teams in Your Team’s Years
The confidence interval is a range of values for which the statistics are within a certain probability. The formula, Confidence Interval = [point estimated – margin of error, point estimated + margin of error] is used to calculate the confidence interval. The margin of error equates to the standard error of the average value that is given by the ratio of standard deviation to the square root of the sample and then multiplied by the appropriate z-score. According to the table below, there is a 95% confidence level for the relative skills from all the teams in the NBA from 2013-2015. Our confidence range is 1502.02 to 1507.18. If we chose to use a different confidence level, the confidence interval would also change.
Table 4. Confidence Interval for Average Relative Skill of Teams in Your Team’s Years
Confidence Level (%)
Confidence Interval
95% Confidence Level
(1502.02, 1507.18)
9.
Confidence Intervals for the Average Relative Skill of All Teams in the Assigned Team’s Years
For this data set, with the 95% confidence interval for the average relative skill for all teams during the 1996-1998 seasons, the range was between 1487.66 and 1493.65. Similarly,
as stated above, if we used different confidence levels, the confidence interval would also change. An increase to the confidence level would widen the interval, whereas a decrease would narrow the interval. Table 5. Confidence Interval for Average Relative Skill of Teams in Assigned Team’s Years
Confidence Level (%)
Confidence Interval
95% Confidence Level
(1487.66, 1493.65)
10. Conclusion
Data analysis is essential for any business or industry. Using sports as an example, creates a visual that can be seen which produces an immediate result to the use of analysis. Seeing how a teams’ production output, from game to game, to the result at the end of the season, we can see how they analyze their strategy and prepare for each game. It helps to understand performance and promote healthy growth and learn from mistakes. By doing data visualizations, measuring central tendency, and variability. We can make raw data into something that can be easily understood and be able to detect patterns and trends.