MAT 243 Project One Summary Report Template (1)

docx

School

Southern New Hampshire University *

*We aren’t endorsed by this school

Course

APPLIED ST

Subject

Mathematics

Date

Feb 20, 2024

Type

docx

Pages

Uploaded by ColonelProton5032

MAT 243 Project One Summary Report MaeLadie Carter Maeladie.carter@snhu.edu Southern New Hampshire University

Note: Replace the bracketed text on page one (the cover page) with your personal information. 1. Introduction: Problem Statement The purpose of this report is to analyze and find patterns in the historical data set given to me. The data gathered from the NBA team Bulls is from 1996-1998 and the data gathered from NBA team Celtics is from 2013-2015. I am going to compare the Celtics to the Bulls by using a comparative analysis to see where the Celtics are doing well and where they can improve. 2. Introduction: Your Team and the Assigned Team The team I chose is the Boston Celtics from 2013-2015 and I was assigned the Chicago Bulls from 1996-1998. Table 1. Information on the Teams Name of Team Assigned Years 1. Yours Celtics 2013-2015 2. Assigned Bulls 1996-1998 3. Data Visualization: Points Scored by Your Team Data visualization is used to study data distributions and trends by plotting variables gathered from data and produces easy to read information about a large data set. In this report, I chose to use the scatterplot that shows the points scored by the Celtics from 2013 to 2015 because you can better see results from a line of fit over the years rather than a histogram of frequency of points scored as an alternative plot. The scatterplot shows that the Celtics have improved over the years and signifies that they have been pretty consistent in scoring.

4. Data Visualization: Points Scored by the Assigned Team The scatterplot for the Bulls from 1996-1998 was chosen because you can better see results from a line of fit. In this plot, the Bulls show a decrease in points scored per game over the years. The distribution is still relatively uniform in shape, showing that they had a consistency of points scored. Because the mean score declines over the years, this signifies that there is a decrease points per game over the years. 5. Data Visualization: Comparing the Two Teams Data visualization is used to compare the two data distributions by showing the teams either side by side in a box plot or overlapping in a histogram. The histogram shown below compares the two teams points per game and I chose this because we can see where they overlap. As we compare the two teams, we see that the Bulls have been performing better over the years in comparison to the Celtics because we see that the Bulls have more games where they have more points per game scored, which is trending their data in a positive direction.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

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 Median Variance Standard Deviation 98.82 99.50 107.67 10.38 Central tendency will show you where most of the data points lie while variability summarizes how far those points from each other. The mean of 98.82 is the sum of the Celtics PPG at home dataset divided by the amount of numbers in the set. The median of 99.82 is the points scored right in the middle of the dataset. The variance of 107.67 is the average of the squared differences of the mean of the dataset and the standard deviation of 10.38 is the square root of the variance. The mean and median are very close which makes the skew for the Celtics PPG appear to be bell shaped. 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 Median Variance Standard Deviation 97.28 96.00 121.43 11.02 The mean of 97.28 is the sum of the Celtics PPG away dataset divided by the amount of numbers in the set. The median of 96.00 is the points scored right in the middle of the dataset. The variance of 121.43 is the average of the squared differences of the mean of the dataset and the standard deviation of 11.02 is the square root of the variance. The mean and median are very close which makes the skew for the Celtics PPG away appear to be bell shaped. By these numbers I see that the Celtics score more points at home than they do at away games. The mean of the PPG at home is higher than the mean of PPG away 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 used to estimate measures of central tendency. It estimates that a population that is sampled multiple times and that have interval estimates calculated for each sample will show the resulting interval approximately lies within the true population X amount of the time. The relative skill confidence interval of 1502.02 to 1507.18 shows that we can use any team from the league and there would be a 95% surety it that the elo of that given team lies between 1502.02 and 1507.18. Using a higher confidence level would give a higher spread between the intervals. 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 95% confidence interval for the data set of the 1996-1998 Bulls is lower than the years obtained for the Celtics. This shows is that the elo of all teams within the timeframe of 1996- 1998 have a lower elo compared to later years. This suggests that there could be an improvement from all teams. The probability that a team had a lesser elo than the Bulls in this timeframe is 50%, which suggests that the Bulls ranked right in the middle during that timeframe. 10. Conclusion The importance of the analysis was to compare the data of the skill level of the 1996-1998 Bulls and my chosen team 2013-2015 Celtics. The data shows that though the Celtics were mor consistent in scoring per game with a mean of 98.82 at home and 97.28 away, the Bulls showed more overall game where the PPG were higher showing that the bulls were relatively better in their time frame.

MAT 243 Project One Summary Report Template (1)

Related Documents