MAT201: SLP #1
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MAT201: Basic Statistics
SLP #1
Joseph Wineman
Trident University International
MAT201: SLP #1
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Introduction
Statistics is the mathematical science that describes the collection, organization and
analysis of raw data. It is of particular importance to organizations because it can be used to
aid leaders in making informed decisions rather than relying on gut feelings.
Data Gathering
I live in the thriving Metropolis of Gadsden, Alabama where I worked for the
Goodyear Tire and Rubber Company for five years. After much soul searching, I recently
decided to make a career change; staying in the manufacturing industry, but trading tires for
The HON Company’s office furniture. Along with the career change came a daily commute
to and from the plant in nearby Cedartown, Georgia. The commute consists of a 55 mile drive
through a combination of state highways, country towns, construction areas, school zones and
a time zone change. Not wanting to be late for work, and still having problems dealing with
the time change and irregular speed limits during my commute, I have decided to track the
amount of time that I spend driving each day from home to work. My desire is to determine
the optimal time to leave for work that allows me to maximize the time I can spend sleeping
without being late. I will utilize the stopwatch on my iPhone to track the time, in minutes,
from the moment that I leave my driveway until the moment that I reach the parking lot at
HON Cedartown. Data was recorded for 10 consecutive work days from July 16 to July 27,
2018, and is recorded below.
MAT201: SLP #1
Sample
Date
Jul 16
Jul 17
Jul 18
Jul 19
Jul 20
Jul 23
Jul 24
Jul 25
Jul 26
Jul 27
1
2
3
4
5
6
7
8
9
10
3
Driving Time
(mins)
128
135
129
135
132
125
131
123
130
125
Departure Time from
Home
3:25
4:15
4:05
4:10
4:15
3:25
4:25
4:30
4:35
3:50
Arrival Time at Work
5:33
6:30
6:14
6:25
6:27
5:30
6:36
6:33
6:45
5:55
Hypothesis
From my limited collection of data points, I believe that my commute takes slightly
more time if I leave the house later than 4:30am. This is due to the additional town traffic and
construction vehicles that are more prevalent as the world around me wakes up. I believe that
this issue will only get worse as we transition from fall to summer due to the school zone that
will be active on my commute after 7:00 am. For my project, I have identified the
independent variable as my departure time from home as it not effected by the other variable,
which I have characterized as my commute time. I have labeled my dependent variable as my
commute time as it varies due to other factors like my departure times. The statistical tools
that will best help me analyze this association are correlation and regression analysis.
Correlation analysis can be utilized to examine the strength of a relationship between two,
numerically measured, continuous variables whereas regression analysis helps estimate the
relationships among variables.
Conclusion
I need to collect more data in order to best represent my commute time as my sample
size is too small (n = 10). I must continue to collect and plot data points to ensure that my
sample averages display a normal distribution. A larger sample size would minimize any
MAT201: SLP #1
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outliers or anomalies which would skew my data. The larger sample size ensures the
normality of data which will provide a better analysis of the sample population. At the end of
this study, I will be able to accurately determine the latest time that I can leave house while
maximizing the amount of time that I can spend sleeping without being late for work.
MAT201: SLP #2
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MAT201: Basic Statistics
SLP #2
Joseph Wineman
Trident University International
MAT201: SLP #2
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Below is the data that was collected regarding my commute from Gadsden, Alabama to
The HON Company, located in Cedartown, Georgia. The commute consists of a 55 mile drive
across multiple counties, through various small towns and includes a time zone change as I cross
the state border from Alabama into Georgia. The data was recorded using the stopwatch
function on my iPhone and took place over ten consecutive work days from July 16 to July 27,
2018.
Date
Driving Time
(mins)
Departure Time from
Home
Arrival Time at Work
1
Jul 16
128
3:25
5:33
2
Jul 17
135
4:15
6:30
3
Jul 18
129
4:05
6:14
4
Jul 19
135
4:10
6:25
5
Jul 20
132
4:15
6:27
6
Jul 23
125
3:25
5:30
7
Jul 24
131
4:25
6:36
8
Jul 25
123
4:30
6:33
9
Jul 26
130
4:35
6:45
10
Jul 27
125
3:50
5:55
Sample
1. Calculate the mean, median, and mode of your collected data. Show and explain
your calculations.
123
125
125 128 129 130 131 132 135
a. Mean: Sum all 10 trips or 1293 / 10 = 129.3
b. Median: Average of 129 and 130 = 129.5
c. Mode: The Modes are 125 and 135
135
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2. Are these numbers higher or lower than you expected? Explain.
These numbers are much higher than I expected. When I accepted the new job with the
HON Company, I thought long and hard about the commute time. Ultimately, I accepted
based on the fact that the plant was only 55 minutes away from my home. Actually
recording the data, and grouping it in such a way to see the central tendencies, I am
actually quite shocked by the information here. However, I do enjoy my work there, so
the commute is not a deterrent.
3. Which of these measures of central tendency do you think most accurately describes
the variable you are looking at? Provide your justification.
I think the mean most accurately describes the variable I am observing. The range of data
is fairly tight across the 10 samples and fairly evenly distributed. If I were to drop the
lowest outlier, the mean and the median would then be 130, which is less than one integer
away from their current values. So, based on my recorded data, it is reasonable for me to
expect my commute to last 130 minutes, or 2 hours and 10 minutes.
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4. Create a box plot to represent the data, labeling and numerating all 5 points on the
box plot. For the plot, you may draw and insert it in your paper as a picture. Make
sure it is legible.
A
B
C
Solution:
A = Minimum - 123
B = 125
C = Median of entire data set – 129.5
D = 132
E = Maximum – 135
A - E = The Range - 12
B - D = The Interquartile Range - 7
D
E
MAT201: SLP #3
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MAT201: Basic Statistics
SLP #3
Joseph Wineman
Trident University International
MAT201: SLP #3
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Below is the data collected in my previous module 1 exercise. The purpose of the data
is to determine the amount of time I take to commute from my home in Gadsden, Alabama to
my place of work, HON Company whose location is in Cedartown, Georgia. This data will
enable me to establish the optimal time am supposed to leave home so that I reach at work in
time when all factors put into consideration.
Date
Driving Time
(mins)
Departure Time from
Home
Arrival Time at Work
1
Jul 16
128
3:25
5:33
2
Jul 17
135
4:15
6:30
3
Jul 18
129
4:05
6:14
4
Jul 19
135
4:10
6:25
5
Jul 20
132
4:15
6:27
6
Jul 23
125
3:25
5:30
7
Jul 24
131
4:25
6:36
8
Jul 25
123
4:30
6:33
9
Jul 26
130
4:35
6:45
10
Jul 27
125
3:50
5:55
Sample
Frequency Distribution table
The frequency distribution is defined as the arrangement or display of outcomes
collected according to their sizes or magnitude as per the observations made. Frequency
distribution partitions large data into small data of classes showing the number of data values
in every class. To construct a frequency distribution table, I will determine the number of
classes to use. From the data collected above, I will go with 7 classes because it will give a
sufficient summary of the data. Then determine the class width which is given by
range/number of classes (Brase, 2013). Subtracting 123 which is the smallest data value from
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135 which is the largest data value and dividing the results by a number of classes I get 2 as
my class width. Below is the obtained frequency table:
class
interval
123-124
125-126
127-128
129-130
131-132
133-134
135-136
(f)
(X)
(FX)
(x̄)
(X-x̄)
(X-x̄)^2
f(X-x̄)^2
1
2
1
2
2
0
2
∑f=10
123.5
125.5
127.5
129.5
131.5
133.5
135.5
123.5
251
127.5
259
263
0
271
∑fX1295.0
129.5
129.5
129.5
129.5
129.5
129.5
129.5
-6
-4
-2
0
2
4
6
36
16
4
0
4
16
36
36
32
4
0
8
0
72
∑ f(X-x̄)^2=152
Standard Deviation
Using the Standard deviation formula and figures obtained in the frequency table
above
SD= √∑ f(X-x̄)^2 =√152/9=√16.88889=4.109
√∑f-1
The standard deviation, therefore, is approximately 4.1
Then:
Variance
Standard deviation is the square root of the variance and therefore using the standard
deviation obtained above, the variance is given by Var=SD^2= (4.1)^2=16.81
Normal Distribution
The normal distribution is a symmetrically skewed distribution (Agostino, 2017). Yes
it is a normal distribution. This is because the mean of the distribution is 129.5 and 50% of
the data values is less than the mean while 50% is greater than the mean. Also using the
standard rule that 68%, 95% and 99.7% of the data values should fall within one standard
deviation, two standard deviations and three standard deviations of the mean respectively and
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using the mean of 129.5and standard deviation of 4.1 as obtained above then 68% of the data
values fall within 129.5-4.1 and 129.5+4.1.
Implications
The results obtained above implies that the process of collecting data hold the
properties or aspects of a normal distribution. It also shows that the data collected can be
relied upon, that is, the degree of confidence in the results obtained is high.
MAT201: SLP #3
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References
Brase, C. H., & Brase, C. P. (2013). Understanding basic statistics. Cengage Learning.
D’Agostino, R. B. (2017). Tests for the normal distribution. In Goodness-of-fittechniques (pp. 367-420). Routledge.
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