CHARRIS - MAT 243 Project One Summary Report
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Southern New Hampshire University *
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APPLIED ST
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Mathematics
Date
Feb 20, 2024
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docx
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Uploaded by CaptainEnergyStork29
MAT 243 Project One Summary Report
Chanelle Harris chanelle.harris@snhu.edu
Southern New Hampshire University
This report aims to study and compare the distribution of key performance metrics. We will use a data set to provide the coaching staff and management with a clear analysis of the performance of our team to improve and prepare for the upcoming season. We will be comparing
our team the Cleveland Cavaliers versus the Chicago Bulls. We will look at games over a few years. Using past data, from past and more current, we will be able to take a deep dive into the differences and be able to see any changes that may be needed to improve our game overall. In reviewing the data and comparing the teams, I will be comparing the mean, median, variance and
standard deviation for the points scored per team at home and on away games.
Being a Cleveland native, I chose the Cleveland Cavaliers for my team and will be analyzing the years 2013-2015. The team chosen for us is the Chicago Bulls and we will be reviewing the years between 1996-1998.
Name of Team
Assigned Years
Cleveland Cavaliers
2013-2015
Chicago Bulls
1996-1998
Data visualization is considered in things like charts, graphs, and maps. We use these tools to provide an easy way to see and understand trends, and patterns in data. I chose the histogram chart because it shows a clear picture of the data spread and is easier to read. Meaning that the mean, mode, and median are exactly the same within a normal distribution. Even though the data between 90 to 110 points form the bell shape there are a few abnormal spikes in frequency, with a slight skew to the left. This tells me that we have had more games in the 90 to 100-point range.
We will continue using the histogram chart to view the Bulls data as well. This way we can compare the two teams, and easily see the differences as well as the similarities. We can clearly see that the Bulls during the years 1996-1998 had more high-scoring games ranging from 95 to 110 points. There are also a few high spikes in scoring, but it is more centralized in the center. The takeaway from this chart shows us that the Bulls during this era had more high-
scoring games on average.
Below we will look at the two charts layered on top of each other. Again this activity is to
compare the frequency of points achieved per game. Data can easily be compared when stacked together. The Bulls are clearly the higher-scoring team, but we can take into consideration that this was the Bull in their prime. We want to be able to take those games and see what we can do to improve our scoring and achieve something of that level.
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Descriptive Statistics for Points Scored by the Cavalier Home Games
Central tendency is how you would find the center of your data, while the variability shows you the dispersion of that data, or how it is spread out. To calculate the central tendency we use the 3 main statistical tools: the mean, median, and mode. The mean of your data is actually the average, the median, which is the number in the middle of your data set once arranged in order, and the mode is the value that occurs most often in your data set. The variance and standard deviation are also very common tools used to analyze your data. The variance is the average of the squared differences from the mean, and the st. deviation is the square root of the variance.
We use these tools to study the pattern of our games. Taking all our high scores, and calculating how often we hit them again. Showing when we may have been on a streak or may have fallen below. Establishing an average, we can guess how each new game will play out. Example, in the table above, we stated that our mean (average) is 99.81. This lets us know that we average approx. 99 points a game, give or take 11 points. That give or take is the measure of Statistic
Value
Mean
99.81
Median
97.0
Variance
131.22
St. Deviation
11.46
the variability of our data set. When looking at game statistics, you will hear people refer to the average mostly. Whether it is points per game, or average points per player, the mean is the most used statistical tool.
Descriptive Statistics for Points Scored by Cleveland Cavaliers in Away Games
Statistic Name
Value
Mean
98.76
Median
98.0
Variance
164.04
Standard Deviation
12.81
See Step 7 in the Python script to address the following items:
●
Summarize all statistics in a formatted table as shown below. Use one row for each statistic. You will need to add rows to the table in order to include all of your statistics.Use the mean and the median to describe the distribution of points scored by your team in away games.
a.
Describe the skew: Is it left, right, or bell-shaped?
b.
Explain which measure of central tendency is best to use to represent the center of the distribution based on its skew.
●
Is your team performing better in games played at home than those played away? Use the mean and the standard deviation to answer this question. What can be deduced by comparing the standard deviation of points scored in home games and points scored in away games?
1.
Confidence Intervals for the Average Relative Skill of All Teams in Your Team’s Years
In the Python script, you calculated a 95% confidence interval for the average relative skill of all teams in the league during the years of your team. Additionally, you calculated the probability that a given team
in the league has a relative skill level less than that of the team that you picked.
See Step 8 in the Python script to address the following items:
●
Report the confidence interval in a formatted table as shown below.
Table 4. Confidence Interval for Average Relative Skill of Teams in Your Team’s Years
Confidence Level (%)
Confidence Interval
XX% (for example, 95%)
(X.XX, X.XX)
*Round off to 2 decimal places.
●
Describe how confidence intervals are generally used in estimating the measures of central tendency for a population.
●
Provide a detailed interpretation of the confidence interval in terms of the average relative skill of
teams in the range of years that you picked.
●
How would your interval be different if you had used a different confidence level?
●
What is the probability that a given team in the league has a relative skill level less than that of the team that you picked? Is it unusual that a team has a skill level less than your team?
Answer the questions in a paragraph response. Remove all questions and this note (but not the
table)
before submitting! Do not include Python code in your report.
2.
Confidence Intervals for the Average Relative Skill of All Teams in the Assigned Team’s Years
In the Python script, you calculated a 95% confidence interval for the average relative skill of all teams in the league during the years of the assigned team. Additionally, you calculated the probability that a given team in the league has a relative skill level less than that of the assigned team.
See Step 9 in the Python script to address the following items:
●
Report the confidence interval in a formatted table as shown below.
Table 5. Confidence Interval for Average Relative Skill of Teams in Assigned Team’s Years
Confidence Level (%)
Confidence Interval
XX% (for example, 95%)
(X.XX, X.XX)
*Round off to 2 decimal places.
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●
Provide a detailed interpretation of the confidence interval in terms of the average relative skill of
teams in the assigned team’s range of years.
●
Discuss how your interval would be different if you had used a different confidence level.
●
How does this confidence interval compare with the previous one? What does this signify in terms
of the average relative skill of teams in the range of years that you picked versus the average relative skill of teams in the assigned team’s range of years?
Answer the questions in a paragraph response. Remove all questions and this note (but not the
table)
before submitting! Do not include Python code in your report.
3.
Conclusion
Describe the results of your statistical analyses clearly, using proper descriptions of statistical terms and concepts.
●
What is the practical importance of the analyses that were performed?
●
Describe what these results mean for the scenario.
Answer the questions in a paragraph response. Remove all questions and this note
before
submitting! Do not include Python code in your report.