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MAT 243 Project One Summary Report Jason Popejoy [email protected] Southern New Hampshire University

The purpose of this summary report is to analyze a large historical data set and find data patterns. I will be using data visualization techniques combined with descriptive statistics to study key variables distributions associated with team performance. This analysis will assist team management make improvements to performance. The data sets I will be using are NBA data sets for the Chicago Bulls, covering the years from 1996 to 1998, and the OKC Thunder covering from 2013 to 2015. In comparing I will be incorporating statistical methods such as data visualization in the form of charts to compare NBA teams, as well as confidence intervals to calculate average relative skills of each team in their given years.

The team I picked for this analysis is the Oklahoma City Thunder and the analysis years picked for me were 2013 to 2015. I was assigned the Chicago Bulls for comparative study. The range of years for the Chicago Bears was 1996 to 1998.

Table 1. Information on the Teams

1. Yours 2. Assigned

Name of Team Oklahoma City Thunder Chicago Bulls

Assigned Years 2013 - 2015 1996 - 1998

Data visualization is used to show information in a format such as a table or chart. Displaying data in this way allows for quick viewing and interpretation, especially of large data sets. The plot I chose is the Histogram. The reason I chose this plot is because to me, it shows the spread of points for the Oklahoma City Thunder and the frequency, or how often, those points were scored.

This histogram shows the points scored over the three-year period from 2013 to 2015, and the frequency those points were scored. By inspecting this histogram, I can see that over the threeyear period the Oklahoma City Thunder scored 102 points with a frequency of 35. I also chose a histogram to show the frequency and the points scored by the Chicago Bulls between 1996 and 1998. To me this plot, like the plot for the Oklahoma City Thunder, is easier to read and has a better breakdown of the points scored during the three-year period and the frequency of those points during that time period. The distribution for the Chicago Bulls shows that over the three-year period, the team scored 104 points with a frequency of 35.

When comparing different data distributions, data visualization can be used to set the data side by side or on top of each other to view the differences. For instance, the two histograms below are used to compare the points scored by the Chicago Bulls in 1996 to 1998 and the Oklahoma City Thunder in 2013 to 2015 and the frequency those points were scored.

I chose this plot because it seemed to show the data in the most useful manner. When comparing these two plots, I was able to see the Oklahoma City Thunder had a higher frequency of points

scored than the Bulls did during their respective time periods.

Table 2. Descriptive Statistics for Relative Skill of the Oklahoma City Thunder Statistic Name Mean Median Variance Standard Deviation

Value 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 Relative Skill of the Chicago Bulls

Statistic Name Mean Median Variance Standard Deviation

Value 1739.8 1751.23 2651.55 51.49

For the three-year period the Bulls had a mean, or average of 1739.8. Their Median, or the middle score was 1751.23. The Bulls had a variance in scores of 2651.55, and the standard deviation for the teams scores was 51.49. This shows that the distribution of scores is bell shaped. Overall, this information shows that the Chicago Bulls had a better skill level during

1996 - 1998 than the Oklahoma City Thunder did during 2013 – 2015. The Bull’s lower variance and standard deviation shows that the Chicago Bulls scores were more consistent than those of the Thunder.

Table 4. Confidence Interval for Average Relative Skill of Teams in the Oklahoma City Thunder’s Years

Confidence Level (%) 95%

Confidence Interval (1502.02, 1507.18)

Confidence intervals are used to estimate uncertainties by giving lower and upper limits that represent a range of values. These values represent the population parameter with a specific level of confidence ("Confidence Interval (CI)"). In terms of the teams during the 2013 – 2015 years, there is a 95% confidence level that the teams will have relative skill falling between 1502.02 points and 1507.18 points. If a different 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 be 99%. The probability that a team has a relative skill less than the Oklahoma City Thunder during the 2013 – 2015 years is 0.0972 or 10%. Table 5. Confidence Interval for Average Relative Skill of Teams in Assigned Team’s Years

Confidence Level (%) 95%

Confidence Interval (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 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 it can be seen that the average relative skill of the Chicago Bulls is better.

When the histogram plots of the two teams are laid over each other, we can really see how similar their scores and frequency were. We can also see the differences more easily. The Thunder and the Bulls seem to average between 90 and 112 points per game with a relatively equal frequency. As the points get higher, the Thunder scores higher points more frequently. The 1996 – 1998 Chicago Bulls relative skill were higher than the relative skill of the Oklahoma City Thunder during 2013 – 2015. The Bulls had a lower standard deviation and variance than the Thunder. This means the Bulls had less variability and their relative skills were more consistent during the 1996 – 1998 years than the Thunder during the 2013 – 2015 years. The mean for the Bulls was more than the mean for the Thunder which means that the bulls scored more points than the Thunder in their respective years. Considering the data, the 1996 – 1998 Chicago Bulls average relative skill is better than the Oklahoma City Thunder in 2013 – 2015.

References

Confidence Interval (CI). (n.d.). Retrieved from https://www.six-sigma-material.com/ConfidenceInterval.html...