MAT 243 Project One Summary Report Template (1)
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Feb 20, 2024
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MAT 243 Project One Summary Report
Melissa Galvan
Email: melissa.galvan@snhu.edu
Southern New Hampshire This summary report's analysis of a sizable historical data set aims to identify data patterns. To examine the important variable distributions linked to team success, I will mix descriptive statistics with data visualization approaches. This analysis will help team management raise performance standards. NBA data sets for the Chicago Bulls, which span the years 1996 to 1998,
and the OKC Thunder, which span the years 2013 to 2015. In order to compare NBA teams, I will use statistical techniques such data visualization in the form of charts and confidence intervals to determine the average relative talents of each club in the relevant years.
The Oklahoma City Thunder was the team I chose for this study, and the years I used for the analysis were 2013 to 2015. I was given the Chicago Bulls to research in comparison. The Chicago Bulls' time frame was from 1996 to 1998.
Table 1. Information on the Teams
Name of Team
Assigned Years
1. Yours
Team Thunder
2013 – 2015
2. Assigned
Team Bulls
1996-1998
Information presented in a format like a table or chart is shown using a visualization. This method of data display makes it possible to quickly analyze and interpret massive data sets. The histogram is the plot I selected. I selected this plot because, in my opinion, it accurately depicts the spread of points scored by the Oklahoma City Thunder as well as their frequency or frequency with which they were scored.
This histogram displays the number of times each point was scored during the course of the three years
from 2013 to 2015. I can see from this histogram that Oklahoma City Thunder scored 102 points with a frequency of 35 over the course of three years. I also decided to use a histogram to display the Chicago Bulls' scoring efficiency and totals from 1996 to 1998. I find that this map out is simpler to read and provides a more detailed summary of the points scored over the course of the three years as well as the regularity of those points throughout that time. It is similar to the layout for the Oklahoma City Thunder.
The Chicago Bulls' delivery reveals that over the course of three years, the team achieved 104 points with an average number of 35.
Data visualization can be used to compare different data distributions by laying the data side by side or on top of one another to see the differences. For example, the two histograms below are used to compare the quantity and frequency of points scored by the Oklahoma City Thunder between 2013 and 2015 and the Chicago Bulls between 1996 and 1998.
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This plot was chosen because it appeared to provide the most informative visualization of the data. I could tell by comparing these two plots that the Oklahoma City Thunder scored more points than the Chicago Bulls did during each of their separate time periods.
To encapsulate the distribution of a data collection, we can utilize the measurements of the central trend and variability. This is accomplished by calculating the information set's mean or average, median, or middle score, variance, or variation in a statistical distribution, and standard deviation. The Mean, or average of the Oklahoma City Thunder's scores over the course of three years, was 1651.28. The center score, or median, was 1659.33. The Thunder's standard deviation was 58.44, indicating that the distribution data is bell-shaped.
Descriptive Statistics for Relative Skill of the Oklahoma City Thunder
Statistic
Value
Mean
Median
Variance
Standard Deviation
1651.28
1659.33
3415.35
58.44
We can use the measures of central tendency and variability to summarize the distribution of a data set. This is done by finding the Mean or average of a data set, the Median middle score for a set, the variance or diversity in a distribution, and the standard deviation. For the Oklahoma City Thunder, the Mean, or average of their scores over the three-year period was 1651.28. The median, or middle score was 1659.33. The standard deviation for the Thunder was 58.44, showing that the distribution data is bell shaped.
Table 3. Descriptive Statistics for Points Scored by Your Team in Away Games
Statistic Name
Value
Mean
Median
Variance
Standard Deviation
1739.8
1751.23
2651.55
51.49
The Bulls' mean, or average, across the three years was 1739.8. Their median score, or average, was 1751.23. The Bulls' score variance was 2651.55, and their team's score standard deviation was 51.49. This demonstrates that the score distribution is bell-shaped.
Overall, the data indicates that the Oklahoma City Thunder had a lower skill level from 2013 to 2015 than the Chicago Bulls did from 1996 to 1998. The Chicago Bulls' lower variance and standard deviation indicate that their performance was more reliable than the Thunder's.
The Confidence Interval for the Oklahoma City Thunder's Years Teams' Average Compared Skill
Confidence Level (%)
Confidence Interval
95%
(1502.02,1507.18)
By providing lower and upper boundaries that indicate a range of values, confidence intervals are utilized to evaluate uncertainty. These numbers (or "Confidence Interval (CI)") describe the population parameter with a certain degree of confidence. There is a degree of trust of 95% that the teams' relative skill will fall between 1502.02 points and 1507.18 points for the years 2013 to 2015. The range of confidence levels would alter slightly and the likelihood that the population mean would be included in the confidence interval would be 99% if a different level of confidence, such as a 99% confidence level, had been selected. Between 2013 and 2015, a team's likelihood of having a worse relative level of expertise than
the Oklahoma City Thunder is 0.0972, or 10%.
Confidence Level (%)
Confidence Interval
95%
(1487.66,1493.65)
In terms of the teams during the 1996 - 1998 years, there is a 95% confidence level that the teams will have relative skill falling between 1487.66 points and 1493.65 points. If a different
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confidence level had been used, such as a 99% confidence level, the confidence interval would change somewhat and the probability that the population mean would be included in the confidence interval would change to 99%. The probability that a team has a relative skill less than the Chicago Bulls during the 1996 - 1998 years is 0.0268 or 3%.When the Chicago bulls in the years 1996 – 1998 are compared with the Oklahoma City Thunder in the 2013 – 2015 years itcan be seen that the average relative skill of the Chicago Bulls is better. We can clearly see how comparable the scores and frequency of the two teams are when we overlay their histogram graphs. The discrepancies are also easier to see. It appears that the Thunder and the Bulls both frequently score between 90 and 112 points each game on average. The Thunder scores higher points more frequently as the points increase. Between 2013 and 2015, the Oklahoma City Thunder's relative skill was higher than the Chicago Bulls' between 1996 and 1998. The variance
and standard deviation were both smaller for the Bulls than for the Thunder. This suggests that compared to the Thunder throughout the years of 2013–2015, the Bulls had less unpredictability, and their relative talents were more stable during that time.