MAT 243 Project One Summary Report Template
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Southern New Hampshire University *
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Mathematics
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Jan 9, 2024
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MAT 243 Project One Summary Report
Southern New Hampshire University
1.
Introduction: Problem Statement
This summary uses descriptive statistics and data visualization tools to examine
performance patterns based on a large set of historical data. The mean, median, min, max,
variance, and standard deviation are the statistical methods that I will use to analyze all data
visualization, desciprive statistics and confidence intervals.
2.
Introduction: Your Team and the Assigned Team
The team that I picked for this analysis is the Boston Celtics from the year 2013-2015.
And the team that assigned to me for the comparative study is Chicago Bulls from the years
1996-1998.
Table 1. Information on the Teams
Name of Team
Assigned Years
1. Yours
Boston Celtics
2013-2015
2. Assigned
Chicago Bulls
1996-1998
3.
Data Visualization: Points Scored by Your Team
Data visualization is the display of data in a format, such as a table or chart, that seeks to
achieve a goal of conveying particulart information to a viewer (zybook, Fall 2023). This
indicates that the main goal of data visualization is to give users an effective way of interpreting
data trends, outliers, and patterns. Graphs, charts, and maps are examples of graphical elements
that can be used to visualize data.
I picked the Boston Celtics point-scoring scatterplot from 2013 to 2015 since it is the simpler
to read of the two and provides a better breakdown of the points. The Boston Celtics teams had a
range between 70 and 120 with an outliner of 90 in 2013, a range between 78 and 120 with an
outliner of 95 in 2014, and a range between 75 and 132 with an outliner of
99 in 2015. The
slope trend line demonstrates that the Boston Celtics performance improves yearly.
4.
Data Visualization: Points Scored by the Assigned Team
I picked the Chicago Bulls' 1996–1998 scatterplot of points scored rather than the histogram
because it is simpler to read and provides a better breakdown of the points. The slope trend line
shows that the team's performance is declining yearly. The team's scores ranged from 72-128
with an outliner of 109 in the year 1996, from 70-135 with an outliner of 109 in the year 1997,
and from 72-122 with an outliner of 100 in the year
1998.
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5.
Data Visualization: Comparing the Two Teams
Boxplot and Histogram were used in data visualization to compare two teams. These tools
compare the average, median, maximum, minimum, and outlier of data set and a variety of
decisions. A boxplot is considerably simpler to read when contrasting the Boston Celtics and
Chicago Bulls.
The Boxplot summarizes the distribution data of two large data points. Chicago
Bulls surpasses Boston Celtics when the two teams are compared. In comparison to the Bulls,
the Celtics have a median somewhere around 98. The Boston Celtics are performing less than
the Chicago Bulls, as shown by the boxplot.
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
98.82
Median
99.50
Variance
107.67
Standard Deviation
10.38
The mean, median, and mode are the central tendency measures. The mode is subject to
standard deviation and variance. Additionally, it identifies the location of the distribution center.
The variability is the difference between values in a dataset and the dataset's center. The two
common measurements of variability are variance and standard deviation.
The Boston Celtics mean is 98.82 signify that the teams average score is calculated by
adding up all scores and dividing
it by the scores count. The median of my choose team is 99.50
which indicated the mid-value score of the team. The varieance of 107.67 represents the average
of the square difference from the means and the standard deviation of 10.38 which is the square
root of variance.
Because the mean and the median to be approxiamtetly equal in the value it shows that
the distribution of scores is bell shaped.
For skewed distributions or distributions with outliers, the median is the most
informative measure of central tendency.
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
97.28
Median
96.00
Variance
121.43
Standard Deviation
11.02
The Boston Celtics' central tendency and variability in away games are presented in the
table above. The Celtics' mean, which displays the average score, is 97.28 based on the table.
The median score for the squad I chose was 96.00, indicating the team's average score. The
variance, which is 121.43, is the average of the square of the difference between the means, and
the standard deviation, which is 11.02, is the variance's square root.
Because the mean and the median to be approxiamtetly equal in the value it shows that
the distribution of scores is bell shaped.
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When compating the results of the score when my teams is playing at home and away, I think
my team performed better when they are home. Because the mean when they are home is 98.82
while away is only is 97.28 which has only 1.54 points difference. Their standard deviation when
they are playing at home is 10.38 while away is 11.02 which means that its more spread out
when they are 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 )
A probability statement is connected with confidence intervals. The confidence interval
measures the level of uncertainty associated with any particular set of statistics. If an actual
population parameter is present inside a confidence interval, the interval is considered accurate.
In order to create a confidence interval, sample statistics and the margin of error are examined.
If you have one small set of data, you must create your confidence interval using the t-
distribution rather than the normal distribution.
Table 4 demonstrates that the average relative skill of teams from 2013 to 2015 is within
the 95% confidence interval. It stands between 1502.02 and 1507.18 points. The confidence
interval would vary if it's a difference in confidence level, such as 90% or 99%, had been
applied, and a 90% or 99% probability would place the Celtics teams' relative skill in the
between the range.
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%
( 1738.62 , 1740.97 )
The table shows that in the year 1996-1998, there is a 95% confidence level that the
Bulls will have relative skill falling between 1738.62 points and 1740.97 points. The confidence
interval would vary if it's a difference in confidence level, such as 90% or 99%, had been
applied, and a 90% or 99% probability that the population mean would be included in the
confidence interval change.
The Chicago Bulls had a higher average relative skill than the Boston Celtics, according
to a comparison of their two confidence levels from the years 1996–1998 and 2013–2015.
10. Conclusion
We can see how teams display outstanding accomplishments and shortcomings
using data visualization, which can be used as a starting point for analysis and improvement.
The Boston Celtics performed better as the years passed from 2013 to 2015, as can be seen
from the scatterplot of points scored by my team. In contrast, the Chicago Bulls, the team
that was assigned to me, did not do as well as the years passed from 1996 to 1998.
The statistical analysis of the descriptive data demonstrates that the Bostos Celtics
perform better at home than in the away games.
We can see that the Chicago Bulls had greater average relative skills from the level of
confidence in the years 1996–1998 than the Boston Celtics did in the years 2013–2015.
11. Citations
ZyBooks
. (Fall 2023).
https://learn.zybooks.com/zybook/MAT-243-J1278-OL-TRAD-
UG.23EW1/chapter/1/section/2
(accessed September 12, 2023).
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