MAT 243 Project One Summary Report Sarah Byerly
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Southern New Hampshire University *
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Feb 20, 2024
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MAT 243 Project One Summary Report
Sarah Byerly
Sarah.Byerly@SNHU.edu
Southern New Hampshire University
1.
In this project I am the designated data analyst for the basketball team. I have discovered a large historical data set on multiple basketball teams. I will be analyzing this information to uncover patterns in the data. My management team along with the team’s coach want to use this information to help improve the team. The people that will be reading the final report are not data analysts therefore I must describe my finding in a way that they will understand. Most of my findings will be focused on the probability that the team can either do better or worse over a certain time compared to the chosen team and their corresponding time. The chosen team that I will compare our team to will be the Chicago Bulls during the 1996-1998 seasons. This is a significant time period for the Bulls and this era was sometimes refered to as their “Dynasty” years. By using this team and time frame I will be setting the bar for success high. I will be comparing the Bulls 1996-1998 to the Los Angeles Lakers 2013-2015 seasons. Below is a table that represents the teams and their respected time periods.
Table 1. Information on the Teams
Name of Team
Assigned Years
1. Yours
Los Angeles Lakers
2013 - 2015
2. Assigned
Chicago Bulls
1996-1998
I will be using Data visualization for displaying my finding in either chart or graph form. This will allow for the data to be viewed easily and interpreted quickly. This is ideal when dealing with large data sets. I chose to use a histogram because it shows the points and how often those points were scored, see raph below. 2.
This graph shows frequency the points were earned from 2013 to 2015. Looking at this histogram we can derive that the Los Angeles Lakers scored 100 points 35 times in three years.
3.
This graph shows the Chicago Bulls points scored during their 1996 to 1998 seasons. This graph, like the Lakers graph, can be interpreted the same way. We see that the Chicago Bulls scored 110 points 30 times over the three years. These data visualizations are intended to be displayed side by side or by overlaying one another. This allows for easy comparison (see histogram below). This graph easily shows the comparison between the points scored for durng the Chicago Bulls 1996-1998 seasons and the Los Angeles Lakers 2013-2015 seasons. 4.
I chose this histogram because of the simplicity of the representation of the facts. When comparing the two sets of data I discovered that the Chicago Bulls had more points scored during their time than the Los Angeles Lakers did.
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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
We can look at the Mean and Median as ways to find the “middle” of the data set. The calculation data was not provided for this information this makes if hard to interperate any furhter. But, we can use this information mto compare these numbers to the numbers generated for ther other team in order to see ther differences.
The Variance is a measure of variability meaning the average of the squared difference of the mean. By taking the square root of the Variance it gives us the Standard Deviation. This information indicated how wide the data set actually is. If we subtract the Median from the Mean
we get the Skew value. For this instance a value of 0.30. This indicates an extreamly small skew to the right. Because of such a small skew we should use the Mean to show the center of distribution. Now that we have the numbers for our team at home we need to compare them too our away games. Statistic Name
Value
Mean
100.71
Median
101.00
Variance
88.16
Standard Deviation
9.39
We will do the same thing we did with the previous information (Table 2). We see that the data is still skewed to the right slightly. This time it has a value of 0.29. This is extreamly close to the previouse table and thus we should use the Mean to show the center of distribution. Looking both
sets of data we see that there is little difference between playing at home verses away. The Mean for home games is 101.70 and away is 100.71. That is only a difference of 0.99. The standard deviation for home games is 12.21 and 9.39 for away games. This indicates that the away games are closerto the mean than the home games thus indicating that the team does better, on average,
at away games. Table 4. Confidence Interval for Average Relative Skill of Teams in Your Team’s Years
Confidence Level (%)
Confidence Interval
95%
(1502.02, 1507.18)
To evaluate uncertainty we use confidence intervals. This provides a range of possible values. Now we can see if it is possible that another team could have a skill level that is less than the Lakers from 2013-2015. There is a 95% Confidence interval level that other teams will have skills that fall bwtween 1502.02 and 1507.18 from the 2013 to 2015 seasons. 5.
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. Table 5. Confidence Interval for Average Relative Skill of Teams in Assigned Team’s Years
Confidence Level (%)
Confidence Interval
95%
(1487.66, 1493.65)
Like the last table we will look at the confidence intervals but this time we will be looking at the Chicago Bulls from 1996-1998. We can see that the liklihoo of a teams relative skills being less than the Bulls was 3%. This indicates that the average skillsof the Bulls from 1996-1998 was better than that of the Lakers from 2013-2015.
When looking at the histograms of the two teams we can see just how close thier frequency and scores actually are. We can also clearly see the differences. The Lakers and the Bulls both seem to alternate between 95 and 110 points per game on a regualr basis. The bulls seem to score more often as the points increase. The relative skills for the 1996-1998 Bulls were higher than that of the 2013-2015 Lakers. There was veary littl difference between the Lakers home and away game statistsics.