University of Windsor
Faculty of Engineering
GENG 2220 Treatment of Experimental Data
Project 1: Simple Data Analysis & Comparison Report
March 6th, 2025
Heer Patel
110151324
Executive Summary
This project provides a comprehensive statistical analysis of 3 different and unique data
sets, using a range of quantitative measures and visual representations in the form of
graphs. The study uses descriptive statistics, confidence intervals, histograms, empirical
rules, five-number summaries, box plots, normal probability plots, and time series graphs
to show the characteristics of each dataset.
In the section on descriptive statistics, we used mean, median, mode, range, maximum
and minimum, standard deviation, skewness, and kurtosis. The empirical rule was used to
determine and assess distribution patterns within one, two, and three standard deviations
of the mean. Histograms and box plots provide a visual representation of the data
distribution, showing the outliers and skewness. Additionally, normal probability plots were
generated to assess data normality and time series graphs were used to show the trends
and fluctuations over time.
Key results show that each dataset has unique distribution characteristics. The first
dataset demonstrates moderate variability with a sharp peak and heavy tails shown by the
high kurtosis value. While the second dataset has a wider spread and numerous peaks,
meaning that it had a lower skewness value and more variability. The third dataset has
multiple outliers and a higher skewness, contributing to the distribution pattern.
The projects underline the importance of statistical data analysis in engineering
applications, particularly in fields such as civil and mechanical engineering, where datadriven decision-making plays a key role in reliability and efficiency. But it has its downsides
for example there are high chances of biasedness and interpretation complexities. But it
remains crucial to problem-solving and quality control.
This project uses Microsoft Excel, this study shows the practicality of statistical techniques
in processing large datasets efficiently and accurately. The findings demonstrate how
statistical methods can be applied in engineering settings to improve system performance,
spot patterns, and guide decision-making.
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Contents
I.
Introduction .........................................................................................................................4
II.
Project Work ........................................................................................................................4
1.
Descriptive statistics ........................................................................................................4
2.
Confidence intervals ........................................................................................................5
3.
Histogram ........................................................................................................................6
4.
Empirical rule ...................................................................................................................7
5.
Five-number summary ......................................................................................................8
6.
Box plot............................................................................................................................8
7.
Normal probability plot .....................................................................................................9
8.
Time Series Graph .......................................................................................................... 10
III.
Results/Discussion ............................................................................................................ 10
IV.
Conclusions....................................................................................................................... 12
V.
References......................................................................................................................... 13
List of Figures
Figure 1- Histogram for data 1 ........................................................................................ 6
Figure 2- Histogram for data 2 ........................................................................................ 6
Figure 3- Histogram for data 3 ........................................................................................ 6
Figure 4- Summary Histogram ........................................................................................ 7
Figure 5- Box plot .......................................................................................................... 8
Figure 6- Normal probability plot for 1 ............................................................................. 9
Figure 7- Normal probability plot for 2 ............................................................................. 9
Figure 8- Normal probability plot for 3 ............................................................................. 9
Figure 9- Time Series Graph for 1 …………………………………………………………………………………….. 10
Figure 10 - Time Series Graph for 2 …………………………………………………………………………………… 10
Figure 11 - Time Series Graph for 3 …………………………………………………………………………………… 10
List of Tables
Table 1- Descriptive statistics......................................................................................... 5
Table 2- Confidence intervals ......................................................................................... 5
Table 3- Histogram Summary Table ……………………………………………………………………………………. 6
Table 4 - Range of Frequencies …………………………………………………………………………………………. 7
Table 5 - Empirical rule .................................................................................................. 7
Table 6 - Five number summary ...................................................................................... 8
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List of Equations
Eq. 1- Confidence level…………………………………………………………………………………………
I.
5
Introduction
This project investigates the use of basic statistical methods, which include box plots, normal
probability plots, histograms, and descriptive statistics, to analyse three different datasets
varying from a range of data. In the project Microsoft Excel is used to compute the data since it
is the most efficient way to analyze hundreds of data values at the same time.
Statistical data analysis is essential to engineering design, manufacturing, and problem-solving
in numerous applications. For example, in civil engineering, statistical analysis is crucial for
uncertainty assessments, risk assessments, optimizing designs and much more. For example,
analysing data from traffic stops aids in the optimisation of urban transport systems, increasing
their effectiveness and lowering traffic.
Furthermore, statistical analysis is essential for quality control and process improvements,
reliability and failure predictions in mechanical engineering. For example, in wind turbines a
statistical approach is used to find failure trends and increase dependability.
Statistical analysis in engineering has drawbacks despite its benefits, for example, it could lead
to biased data and cause errors, it could also be difficult to interpret the concepts and cause
misinterpretation in the results, it also relies heavily on assumptions and has lots of limitations.
But its contributions to improved decision-making, system dependability, and performance
optimisation are still noteworthy.
Overall, this project emphasises the value of statistical analysis in engineering by showing how
it can be used practically to solve problems and advance the discipline.
II.
Project Work
1. Descriptive statistics
In this portion of the project we determined the maximum and minimum values
using the MIN() and MAX() functions, respectively. Subtracting the maximum and
minimum values gave us the range. After doing this we used the the COUNT()
function to determine the total number of values in each data sets. The mean and
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median were calculated using the AVERAGE() function and MEDIAN() function,
respectively. To find the mode, we used the MODE() function. (Allan, G 20221
)Standard deviation was computed using the STDEV.S() function, while kurtosis was
determined using the KURT() function. Skewness was assessed using the SKEW()
function. These analyses provided valuable insights into the central tendency,
spread, and shape of the dataset, facilitating a comprehensive understanding of its
characteristics. (Zaiontz, 2022)
Table 1- Descriptive statistics
2. Confidence intervals
For this project only the confidence levels at 95% and 99% were calculated using
the respective z-values of 1.960 and 2.576 (Gerards, 2019). Utilizing the mean,
standard deviation, and the number of data points, the confidence intervals were
computed using the formula:
Eq. 1- Confidence level
=Mean ± (Z score) * (Standard deviation/sqrt(Count()))
Table 2- Confidence intervals
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3. Histogram
Figure 1- Histogram for Data set 1
Figure 2- Histogram for Data set 2
Figure 3- Histogram for Data set 3
Table 3 - Histogram range, data, lower and upper limits
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Histograms were generated using Excel's built-in Histogram feature, facilitating clear
visualization of the data distributions. The summary graph below depicted below was
created using Excel's 2D bar graph function, showing the number of values from a range of
70 per bin.
Figure 4- Summary histogram
Table 4 – Showing range and frequency for the data
sets and histogram
4. Empirical rule
To determine the percentage of data within (±1, ± 2, ± 3) standard deviations from
the mean, the lower and upper limits were calculated using the formula mean ± (1,
2, 3)(standard deviation), where the minus sign indicates the lower limit and the
plus sign indicates the upper limit.
Table 5- Empirical rule
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5. Five-number summary
The five-number summary, including Q1, Q2 (median), Q3, minimum, and
maximum, was derived using Excel's QUARTILE.INC function. This function takes
the dataset array and quartile parameter as inputs, where 0 represents the
minimum, 1 represents Q1, 2 represents Q2, 3 represents Q3, and 4 represents the
maximum value.
Table 6- Five number summary
6. Box plot
The box plots for each dataset were created using Excel's built-in box plot function.
The figure below displays the box plots for all three datasets in a single graph,
providing a visual representation of the distribution characteristics and variability
within each dataset.
Figure 5- Box plot for all 3 data
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7. Normal probability plot
Figure 6- Normal probability plot for Data set 1
Figure 7- Normal probability plot for Data set 2
Figure 8- Normal probability plot for Data set 3
The following steps were used to construct the normal probability plot. First, the
data was arranged in ascending order and assigned ranks using the RANK() function
in excel. Then, the cumulative probability was calculated using the formula (first
value from data - 0.5) / total number of data. Then, the formula
=NORM.S.INV(cumulative probability) was employed to determine the Z score. Then
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the scatter plot of the Z-scores VS. data set was created, and a trendline was added,
displaying the equation and the coefficient of determination (r-squared value).
8. Time Series Graph
Figure 9 – Time series plot for Data set 1
Figure 10 – Time series plot for Data set 2
III.
Figure 11 – Time series plot for Data set 3
Results/Discussion
Data set 1 has a mean of 80.28 and a median of 78.40, revealing a close alignment between
central tendency measures. The data has no mode meaning that the data is unimodal and
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allo values are unique. The data has a skewness of 12.48 and a standard deviation of 30.30
implies relatively low variability around the mean. However, the high kurtosis value of
194.37 indicates a distribution with a sharper peak and a heavier tail on either side
compared to a normal distribution. The histogram confirms this observation, displaying a
distinct peak with data points and a smaller peak to the left.
Data set 2 has a mean of 201.01 and a median of 200.66, indicating a smaller positive
skewness given that the mean is slightly higher than the median. Just like the first data set
there is no mode making the data unimodal, which in turn means that all the value are
unique. The data has a skewness of 1.42 which is a positive skewness and has a standard
deviation of 65.03 indicates greater variability compared to data set A. The kurtosis value of
10.17 suggests a distribution a high peak with 2 other peaks with a slightly smaller
frequency. The histogram for data B reflects this, displaying 1 high peak and one peak on
both sides with almost similar frequencies.
Data set 3 has a mean of 7.98 and a median of 4.85. Like the previous data this set also has
no mode meaning that it has unique values and is unimodal. It has a skewness of 8.35, the
data shows a positive skewness, slightly lower than the first data set and very high
compared to the 2nd. It has a standard deviation of 13.08 indicating less variability
compared to Data sets 2 but slightly like data set 1. The kurtosis value of 96.02 suggests a
high peak with a smaller peak on either sides. The histogram for data set 3 reflects on the
statement.
The normal probability plots prove these observations. All 3 normal probability graphs have
a trendline that follows the data sets meaning that the data shows normality. Similarly, the
time series graph data shows that all the data is similar to each other but some peaks show
the data has outliers. The first and second data set shows 1 big peak with slightly 1 or 2
smaller peaks which are the outliers while the third data set shows 2 big peaks and various
small peaks showing numerous outliers.
The box plots also act as proof to the statement above about the time series graph showing
the number of outliers in both data set 1 and 2 have 2 outliers that are very far away from
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the median and mean. Where as on the third data set there are many outliers and the rest
of the data is similar to each other and close to the mean and median.
IV.
Conclusions
The significance of statistical data analysis in engineering applications is highlighted by this
project, which shows how to analyse three distinct datasets using a variety of statistical
techniques. To fully comprehend the features of each dataset, descriptive statistics, box
plots, normal probability plots, histograms, empirical rules, five-number summaries, and
time series graphs were employed.
The results show that, according to their different means, medians, skewness, and kurtosis
values, each of the three datasets has distinct distribution patterns. These distributions
were shown using histograms and box plots, which verified that each dataset contained
outliers, skewness, and kurtosis variations. These conclusions were further supported by
the normal probability plots, which showed that there were occasional deviations from the
datasets' normal distribution even if they generally had one. Additionally, the time series
visualisations clarify the trends and changes in the data over time.
This study highlights the importance of statistical analysis in engineering problem-solving,
despite its difficulties and possible biases. Process optimisation, dependability, and overall
system performance all depend on the capacity to assess uncertainty, identify trends, and
make data-driven decisions. Microsoft Excel was a useful tool for efficient large-scale data
analysis.
In conclusion, the statistical techniques used in this study are crucial for assessing
engineering data and offer valuable insights into the dataset's characteristics. By enhancing
decision-making, quality assurance, and system optimisation, these methods demonstrate
the importance of statistical analysis in engineering domains.
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V.
References
Gerards, J. (2019) How to calculate proportion for normal distribution, Sciencing. Available
at: https://sciencing.com/calculate-proportion-normal-distribution-8723987.html
(Accessed: 6th March 2025).
Allan, G (2022) Elementary Statistics: A Step By Step Approach ISE. Available at:
https://www.mheducation.ca/product/elementary-statistics-a-step-by-stepapproach-ise-9781265248123-can-group (Accessed: 6th March 2025).
June 10, 2023 (2023) How to interpret excess kurtosis and skewness, SmartPLS. Available
at: https://www.smartpls.com/documentation/functionalities/excess-kurtosis-andskewness/ (Accessed: 6th March 2024).
October 13, 2023 (2023) How is statistics used in engineering?, Michigan Technological
University. Available at: https://onlinedegrees.mtu.edu/news/how-statistics-usedengineering (Accessed: 6th March 2025).
Zaiontz, C. (2022) Symmetry, Skewness and Kurtosis, Real. Available at: https://realstatistics.com/descriptive-statistics/symmetry-skewness-kurtosis/ (Accessed: 6th
March 2025).
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