Pham Khoa Vien GBS190915 GBS0903 Truong Ngoc Thinh
Pham Khoa Vien GBS190915 GBS0903 Truong Ngoc Thinh
Pham Khoa Vien GBS190915 GBS0903 Truong Ngoc Thinh
Student declaration
I certify that the assignment submission is entirely my own work and I fully understand the consequences of plagiarism.
Student Signature
Grading grid
P3 P4 P5 M2 M3 M4 D1 D2 D3
1
2
Description of activity undertaken
3
Assessor name:
4
Signature & Date:
Unit Assessor
Submission Date
Submission Format
Format
5
• This assignment is an Individual report.
• You must use font Times New Roman, size 12, set number of the pages
and line spacing at 1.5 lines. Margins must be: left: 2.5 cm; right: 2 cm; top: 2 cm and
bottom: 2 cm.
• You should use in-text references and a list of all cited sources at the end of the essay by
applying the Harvard referencing style.
• The recommended word limit is 3500-4000 words (+/-10%), excluding the tables, graphs,
diagrams, appendixes and references. You will not be penalized for exceeding the total
word limit.
• The cover page of the report has to be the Assignment front sheet 2 (to be attached with
this assignment brief).
Submission
• Students are compulsory to submit the assignment in due date (slot 36) and in a way
requested by the Tutor.
• Remember to convert the word file into PDF file before the submission on CMS.
Note
• The individual Assignment must be your own work, and not copied by or from another
student.
• If you use ideas, quotes or data (such as diagrams) from books, journals or other sources,
you must cite your sources, using the Harvard style.
• Make sure that you understand and follow the guidelines to avoid plagiarism. Failure to
comply with this requirement will result in a failed assignment.
LO2. Analyse and evaluate raw business data using a number of statistical methods.
LO4. Analyse and evaluate raw business data using a number of statistical methods.
6
Assignment Brief and Guidance
*This assignment guidance is for reference only and can be customized by the tutor to meet
specific needs
Assignment Scenario
You are assumed as a Research Analyst. Your company is planning to improve the information
system and the decision-making process by applying several statistical methods.
Precisely, you are required to demonstrate your understanding by applying statistical techniques
in business planning and operations management (if possible, with the same dataset from the
first assignment).
Introduction (inheriting from Assignment 1 and developing the additional methodology applied
in this assignment)
3. Methodology (changed)
Main contents
1. Analysing and evaluating qualitative and quantitative raw business data from a range of
examples using appropriate statistical methods
Identify the differences between qualitative and quantitative raw data analysis.
Inferential statistics illustrating the differences between population and sample based
7
on different sampling techniques and methods:
One sample T-test: Estimation and Hypotheses testing.
Two sample T-test and Independent Sample T-test: Estimation and Hypotheses
testing.
8
Measuring the association between two variables (from the dataset)
by using SPSS software or Excel for raw data analysis:
Applying fitting techniques (correlations, regression analysis and
simple forecasting).
Critically evaluating the pertinent applications of different statistical methods in terms
of relevant business and economic data/information and comparing with variety of
applications from other published sources.
Critically evaluating the differences in application among descriptive, exploratory and
confirmatory analysis techniques of business and economic data in general.
2. Applying a range of statistical methods used in business planning for quality, inventory and
capacity management
Measuring the variability in business processes or quality management
Inference
Analysing data and interpreting results by using frequency distribution tables, graphs,
and charts (pie chart, bar chart, histograms with normal curve and scatter plots).
Giving out the strengths and weaknesses of using different types of charts and tables
for disclosing analytical outcomes.
Choosing the most effective way of communicating the results of your analysis and
variables and explaining for the selection.
Conclusion
9
planning processes in your organisation.
Unit Assessment Criteria
P5 Using appropriate M4 Justify the rationale for D3 Critically evaluate the use
charts/tables communicate choosing the method of of different types of charts
findings for a number of given communication. and tables for communicating
variables. given variables.
10
Introduction
Assuming the role of Research Analyst, the organization intends to use a variety of statistical
methodologies to strengthen the information system and decision-making process. To be more
specific, utilizing statistical tools in business planning and operations management is required to
demonstrate understanding (if possible, with the same dataset from the first assignment). The
following requirements will be accomplished in order for this assignment to be completed:
Introduction (inheriting from assignment first and developing the additional methodology applied in
this assignment), It is necessary to demonstrate the background and reasons for selecting the issue.
The study's goals, scope, and significance, Methodology, and Structure of the report.
A. Analyze and evaluate raw business data using a number of statistical methods
1.Analyseand evaluate qualitative and quantitative raw business data from a range of
examples usingappropriatestatisticalmethods.
Quantitative and qualitative data are the two types of data available. Qualitative data is gathered
through qualitative research, while quantitative data is gathered through quantitative research. They
use qualitative and quantitative analysis for each appropriate type of data to analyze it. Both are
important techniques for gathering and interpreting data in research. The differences between two
types of analysis are shown in the table below.
11
the collection
and analysis of
previous data
Purpose interpret social interactions and Test hypotheses, check the cause and
understand effect . Develop predictions for future
Sampling Small, selected intentionally Large and selected randomly
Focus Descriptive data Numerical data
Analysis Inductive (by the researcher) Deductive(by the statistical methods)
Researchtype Exploratory Conclusive
Datatype Words, images, objects Numbers and statistics
Dataform Open-ended responses, interviews, For data collection, precise
measurements using structures and
participant observations, field notes
validated instruments are required.
Result Particularfindings, less generalizable Generalizable findings, can be applied
to theother applications
Advantages Because human interactions are more Quantitative research may be very
complex than molecular reactions in a familiar to you from your science
beaker, qualitative research is frequently classes, where you learned and
used to conduct social and behavioral practiced using the scientific method.
studies. Qualitative research is Deductively forming a hypothesis
distinguished from quantitative research derived from theory is used to
by subjectivity, nonrandom sampling, and investigate a problem or question.
a small sample size. The ability to deeply Your hypotheses will be supported or
probe and obtain rich descriptive data rejected based on controlled,
about social phenomena through objective testing and
structured interviews, cultural immersion, experimentation. To reduce bias when
case studies, and observation, for collecting and analyzing data, each
example, is a major advantage of step is standardized. The results are
qualitative research. Ethnography, valid, reliable, and generalizable to a
narratives, and grounded theory are some larger population, which is a major
examples. (Dowd, 2018) benefit of this approach. Quantitative
research is beneficial.
12
for studies
involving
numbers, such as assessing the
effectiveness of a new blood pressure
medication or measuring achievement
gaps between different groups of
students. (2018. Dowd)
Disadvantage Due to the time-consuming nature of While quantitative research methods
s gathering and analyzing field notes, work well in the lab under carefully
transcribing interviews, identifying controlled conditions, observing
themes, and studying photographs, human behavior in natural settings is
qualitative studies often take longer to more difficult. Errors in survey
complete. Studies are difficult to replicate instruments, such as measurement
or generalize to the general public. The errors and poor sampling techniques,
researcher's conclusions may be are common. Another disadvantage is
influenced by conscious or unconscious that quantitative research
bias. Some researchers may dismiss necessitates the use of numbers,
qualitative findings as anecdotal which can be difficult to quantify in
information because they lack rigorous some cases. It would be difficult, for
scientific controls and numerical data. example, to create an effective survey
(Dowd, 2018) with closed-ended questions about
how people fall in love. (Dowd, 2018)
A mixed method approach takes advantage of both quantitative and qualitative methods while
balancing out their disadvantages. A principal, for example, who wants to improve relations with
school-age children's parents, might conduct a mixed method study. To begin, the principal would
send a school climate survey to parents, asking them to rate their satisfaction with the school and the
quality of instruction provided. The principal would analyze the data and identify areas that needed
more investigation, such as parent complaints about the school's response to bullying incidents. After
that, focus groups could be organized to collect qualitative information from parents in order to
better understand their concerns. (Dowd, 2018)
2. Evaluate the differences in application between descriptive statistics, inferential
statistics and measuring association.
13
Statistical Analysis uses past data in the form of dashboards to show "What
happened?" Data collection, analysis, interpretation, presentation, and
modeling are all part of statistical analysis. It examines a group of data or a subset of data. This type
of analysis is divided into two categories: descriptive analysis and inferential analysis.
Descriptive Statistics: Descriptive statistics is a branch of statistics that quantifies the important
characteristics of a dataset. It uses measures of central tendency, such as mean, median, and
mode, as well as measures of dispersion, such as range, standard deviation, quartile deviation,
and variance, to describe properties. The researcher summarizes the data in a useful manner,
using numerical and graphical tools such as charts, tables, and graphs to accurately represent
data. Furthermore, the diagrams are accompanied by text that explains what they represent.
Inferential Statistics: The goal of inferential statistics is to generalize from the sample to the
population, which means that the results of the sample analysis can be extrapolated to the larger
population from which the sample was drawn. When it is not possible to query each and every
member of the universe, it is a convenient way to draw conclusions about the population.
Because the sample chosen is representative of the entire population, it must include key
characteristics of the population. By employing probability theory, inferential statistics is used to
determine the probability of properties of the population based on the properties of the sample.
Statistical models such as analysis of variance, chisquare test, student's t distribution, regression
analysis, and others are used to generate inferential statistics. Inferential statistics methods
include: Parameter estimation and hypothesis testing
Comparison
To begin with, descriptive statistics is a branch of statistics concerned with describing the population
under investigation. Inferential statistics is a type of statistics that focuses on drawing population-
level conclusions from sample analysis and observation. Second, descriptive statistics gathers,
organizes, analyzes, and presents data in an understandable manner. Inferential statistics, on the
other hand, compares data, tests hypotheses, and forecasts future outcomes. Finally, descriptive
statistics uses a diagrammatic or tabular representation of the final result, whereas probability is
used to display the final result. Fourth, descriptive statistics are used to describe a situation, whereas
inferential statistics are used to explain the likelihood of an event occurring. Finally, descriptive
statistics summarizes the sample by explaining previously known data. Inferential statistics, on the
14
other hand, tries to reach a conclusion in order to learn more about the
population, which goes beyond the data available.
Descriptive statistics is concerned with illustrating your current dataset, whereas inferential statistics
is concerned with making assumptions about a population outside of the dataset under investigation.
While descriptive statistics provide a summary of the data that the researcher has actually studied,
inferential statistics make generalizations based on the data that they have been given.
The author delves into the differences between descriptive and inferential statistics when it comes to
business data:
I. Descriptive statistics
Measures of central tendency: is a single value that represents the data set's center point. This
value is also referred to as a dataset's "central location." Using different methods, each of these
15
measures locates the dataset's center. One of these three measures may
be better to use than the other two depending on the type of data you're
analyzing. (Zach, 2018)
Mean: The mean is the most commonly used measure of central tendency. To find the dataset's
mean, add all of the individual values together and divide by the total number of values. The mean is
calculated by taking into account all of the data's values. The mean changes if they change any of
their values. The mean, on the other hand, does not always accurately locate the data's center.
Mean = (sum of all values) / (total of values)
For example: The author recommends the following dataset, which shows monthly sales and
marketing. spending for the previous year's twelve months.
Descriptive Statistics
16
2
1
Sales 502729 582746 545691,17
2
Valid N (listwise) 1
2
Median: The median is the value in a dataset that is in the middle. By arranging all of the individual
values in a dataset from smallest to largest and finding the middle value, you can find the median.
The median is the middle value when there are an odd number of values. The median is the average
of the two middle values when there are an even number of values.
For example, to determine the median amount of money spent over the course of eleven months last
year. The author can sort the data in any order from smallest to largest.
The median is simply the middle value because they have an odd number of values: 49546 and
544066. of advertising and sales in June.
Consider whether they have eight distinct areas. Because there are an even number of values in this
case, the median is simply the average of the two middle ones: 52825.5 for advertising and 548865
for sales.
17
Mode: In a dataset, the mode is the value that appears the most frequently. No mode (if no value
repeats), one mode, or multiple modes can be present in a dataset.
The following dataset, for example, has no mode:
They've seen how the mean, median, and mode all measure the central location of a dataset, or its
"typical value," in different ways:
18
+ Median: Finds the dataset's middle value.
+ Mode: Finds the value that appears the most frequently in a dataset.
Measuresofvariability
A summary statistic that represents the amount of dispersion in a dataset is known as a measure of
variability. What is the degree of dispersion of the values? Measures of variability define how far
away the data points tend to fall from the center, whereas measures of central tendency describe the
typical value. Variability is discussed in the context of a value distribution. A low dispersion value
indicates that the data points are tightly clustered around the center. They tend to fall further away
when there is a lot of dispersion. 2021 (Frost) The range is the simplest and most straightforward
measure of variability to calculate and comprehend. The difference between the dataset's largest and
smallest values is the dataset's range.
While the range is straightforward, it is based solely on the dataset's two most extreme values,
making it vulnerable to outliers. Even if one of those numbers is out of the ordinary, it has an impact
on the entire range.
Range= Largest value- Smallestvalue
Descriptive Statistics
Variance: The average squared difference of the values from the mean is known as variance. By
comparing each value to the mean, the variance includes all values in the calculation. Calculate a set
of squared differences between the data points and the mean, add them up, and divide by the
number of observations to get this statistic. As a result, the average squared difference is used.
Variance is defined as the mean of the square of deviations from the mean.
Descriptive Statistics
19
N Minimum Maximum Mean
Variance
1
Advertising 40937 63246 52232,25 76676557,477
2
1 738550374,69
Sales 502729 582746 545691,17
2 7
1
Valid N (listwise)
2
Standard deviation: Standard deviation is a statistic that uses the square root of the variance to
determine how far a group of numbers is from the mean. Because outliers are weighted more heavily
than data closer to the mean, squares are used in the calculation of variance. This calculation also
prevents above-the-mean differences from canceling out below-the-mean differences, resulting in a
variance of zero.
By calculating the variation between each data point relative to the mean, standard deviation is
calculated as the square root of variance. There is a higher deviation within the date if the points are
further from the mean; if they are closer to the mean, there is a lower deviation.So the more spread
out the group of numbers are, the higher the standard deviation. (Anderson, 2021)
Descriptive Statistics
20
1
Advertising 40937 63246 52232,25
2 8756,515
1
Sales 502729 582746 545691,17 27176,283
2
Valid N (listwise) 1
2
Coefficient of Variation: The coefficient of variation (CV) is a statistical measure of data points'
dispersion around the mean in a data series. The coefficient of variation is a useful statistic for
comparing the degree of variation between two data series, even if the means are drastically
different. It represents the ratio of the standard deviation to the mean. (Anderson, 2021)
It is the standard deviation to mean of data ratio. It is a percentage-based metric that is used to
compare two or more data sets. The coefficient of variation formula or calculation can be used to
calculate the difference between a stock, commodity, or bond's historical mean price and current price
performance in comparison to other assets.
II. Inferential Statistics
The set of data is collected and selected from a statistical population with the help of some defined
procedures in statistics and quantitative methodology. Population and sample data sets are the two
types of data sets. In order to calculate the mean deviation, variance, and standard deviation,
researchers must first determine whether they are referring to the entire population or only sample
data.
21
Population: Surbhi S has written the following definition of population: “In simple terms,
population refers to the totality of all elements under study that share one or more common
characteristics, such as all people living in India. Animals, events, objects, buildings, and other
things can all be considered part of the population. It can be any size, and population size
refers to the number of elements or members in a population; for example, if India has a
population of 100 million people, the population size (N) is 100 million. The following are the
various types of populations:
Finite Population: The population is said to be finite when the number of elements in the
population is fixed, allowing it to be counted in its entirety.
1. Infinite Population: When a population's number of units is uncountable, making it
impossible to observe all of the universe's items, the population is said to be infinite.
2. Existent Population: Existent population refers to the population of objects that exist in
reality.
3. Hypothetical Population: "A hypothetical or imaginary population is one that exists only in
the mind." (S, 2017)
Sample: “By the term sample, we mean a part of population chosen at random for participation in
the study. The sample should be chosen in such a way that it accurately represents the population in
all of its characteristics and is free of bias in order to produce a miniature cross-section, as the sample
observations are used to make population-wide generalizations. In other words, a'sample' is made up
of respondents chosen from a population, and the process of selecting respondents is known
as'sampling.' The sampling units are the units under investigation, and the sample size is the number
22
of units in a sample. Samples are commonly used in statistical testing when the
sample size is too large to include all members of the population under study."
(S, 2017).
There are two types of sampling in general. Probability sampling and non-probability sampling are
the two types of sampling.
Probability(Random) sampling: involves a random selection process that allows you to draw strong
statistical conclusions about the entire group. The term "probability sampling" refers to the fact
that every member of the population has an equal chance of being chosen. It's mostly used in
quantitative studies. Probability sampling techniques are the best option for producing results
that are representative of the entire population. A probability sample can be divided into four
categories.
"Every member of the population has an equal chance of being selected in a simple random sample."
The population as a whole should be included in your sampling frame. You can use random number
generators or other techniques that are entirely based on chance to conduct this type of sampling.
For instance, suppose you want to choose a simple random sample of 100 Company X employees.
You assign a number from 1 to 1000 to each employee in the company database, and then choose
100 numbers using a random number generator.” (McCombes, 2019)
2) Systematic sample:
"Systematic sampling is similar to simple random sampling, but it is generally easier to carry out.
Every person in the population is assigned a number, but rather than assigning numbers at random,
individuals are chosen at regular intervals.
For instance, the company's employees are listed alphabetically. You choose a starting point at
random from the first ten numbers: number 6. Every tenth person on the list is chosen from number
6 onwards (6, 16, 26, 36, and so on), resulting in a sample of 100 people.
If you use this technique, make sure the list doesn't contain any hidden patterns that could skew the
sample. If, for example, the HR database groups employees by team and team members are listed in
23
order of seniority, there's a chance your interval will miss people in lower-level
positions, resulting in a sample that's skewed toward senior employees."
(McCombes, 2019)
3) Stratified sample
“Stratified sampling entails segmenting the population into subgroups that may differ significantly. It
allows you to draw more precise conclusions by ensuring that each subgroup in the sample is
properly represented. You divide the population into subgroups (called strata) based on the relevant
characteristic when using this sampling method (e.g. gender, age range, income bracket, job role).
You calculate how many people should be sampled from each subgroup based on the population's
overall proportions. Then you select a sample from each subgroup using random or systematic
sampling.
For example, there are 800 female employees and 200 male employees at the company. You sort the
population into two strata based on gender to ensure that the sample reflects the company's gender
balance. Then you select 80 women and 20 men at random from each group, giving you a
representative sample of 100 people." (McCombes, 2019)
4) Cluster sample
"Cluster sampling also entails dividing the population into subgroups, but each subgroup should have
characteristics in common with the entire sample." Rather than sampling individuals from each
subgroup, you choose entire subgroups at random. If it's feasible, you could include every single
person from each sampled cluster. If the clusters are large, one of the above techniques can be used
to sample individuals from within each cluster. This method is useful for dealing with large, dispersed
populations, but it increases the risk of sample error because there may be significant differences
between clusters. It's difficult to know if the sampled clusters are genuine.
For instance, the company has offices in ten different cities across the United States (all with roughly
the same number of employees in similar roles). You don't have the time or resources to visit every
office to collect data, so you use random sampling to choose three offices as your clusters."
(McCombes, 2019)
Non-probability sampling: Non-random selection based on convenience or other criteria is used to
collect data quickly. Individuals are chosen based on non-random criteria in a non-probability
sample, and not every individual has a chance of being included. This sample is easier to obtain
and less expensive, but it has a higher risk of sampling bias. As a result, the population inferences
24
you can draw are weaker than with probability samples, and your
conclusions may be more limited. Even if you're working with a
nonprobability sample, you should try to make it as representative of the population as possible.
In exploratory and qualitative research, non-probability sampling techniques are frequently used.
The goal of this type of research is to develop an initial understanding of a small or under-
researched population, rather than to test a hypothesis about a large population. Nonprobability
samples are divided into four categories.
1) Convenience sample
A convenience sample is made up of people who are most easily accessible to the researcher." This is
a quick and low-cost way to collect preliminary data, but there's no way to know if the sample is
representative of the population, so the results aren't generalizable.
For example, suppose you're interested in learning more about student support services at your
university, so you ask your classmates to complete a survey on the subject after each of your classes.
This is a convenient way to collect data, but the sample is not representative of all students at your
university because you only surveyed students who were taking the same classes as you at the same
level. (McCombes, 2019)
2) Voluntary response sample
Similar to a convenience sample, The convenience of access is a major factor in a voluntary response
sample. People volunteer themselves rather than the researcher selecting and directly contacting
them (e.g. by responding to a public online survey). Because some people are inherently more likely
to volunteer than others, voluntary response samples are always skewed. Consider the following
scenario: You distribute the survey to all students at your university, and many of them choose to
participate. Although this can provide some insight into the topic, the people who responded are
more likely to have strong opinions about student support services, so you can't be sure that their
views are representative. (McCombes, 2019)
3) Purposive sample
This type of sampling, also known as judgment sampling, entails the researcher using their knowledge
to choose a sample that is most useful to the study's goals. It's frequently used in qualitative
research, especially when the researcher wants to learn more about a specific phenomenon rather
25
than making statistical inferences, or when the population is small and specific.
In order to be effective, a purposive sample must have clear inclusion criteria
and rationale.
For example, if you want to learn more about the perspectives and experiences of disabled students
at your university, you purposefully select a group of students with varying levels of support in order
to collect a diverse set of data on their interactions with student services. (McCombes, 2019)
4) Snowball sample
Snowball sampling can be used to recruit participants via other participants if the population is
difficult to reach. As you meet more people, the number of people to whom you have access
"snowballs." Consider the following scenario: You're conducting research into homelessness in your
city. Probability sampling is impossible because there is no list of all homeless people in the city. You
meet one person who agrees to take part in the study, and she connects you with other homeless
people in the area who she knows. (McCombes, 2019)
Comparison
Some of thekey differences between population and sample are clearly given below:
Comparison Population Sample
Meaning Collection of all the units or elements A subgroup of the members of the
that possess common characteristics
population
Includes Each and every element of a group Only includes a handful of units of
population
Characteristics Parameter Statistic
Datacollection Complete enumeration or census Sampling or sample survey
Focus Identification of the characteristics Making inferences about the
population
To summarize: The sample is the group of people who take part in the study, while the population is
the larger group of people who will be affected by the findings. The researchers can compare their
sample to an aquarium, and their population to the ocean. The sample is a small part of a much
larger ocean that the scientists are trying to comprehend. They will benefit from being able to
distinguish between these two concepts as they navigate the methodological details of their
dissertation.
26
Thedifferencesbetweensamplingtechniquesandmethods
One sample T-test: The one-sample T-Test is a population mean hypothesis test
that is used when researchers want to investigate the relationship between a quantitative
population's mean and a specific value.
One-Sample Statistics
Test Value =
12
t df Sig. (2- Mean 95% Confidence Interval of
tailed) Difference the
Difference
Lower Upper
Advertisin 20,658 1 ,000 52220,250 46656,63 57783,87
g 1
Sales 69,557 1 ,000 545679,167 528412,18 562946,15
1
Independent Sample T-test: The Independent-Samples T-Test is a population mean hypothesis test
that is used when researchers want to test the hypothesis that two population means are equal
based on two independent samples drawn from two independent samples. The researchers use one
quantitative variable to calculate the average and one qualitative variable to divide the group into
comparisons in the Independent-Samples T-Test.
27
For example:
If the variance between the sexes is different, we will use the pink sig T-Test value in the
Equal variances not assumed row if Levene's Test sig is less than 0.05.
+ With a sig T-Test value of 0.05, we can conclude that there is a statistically significant
difference in respondents' satisfaction levels between genders.
+ Because the sig T-Test value is greater than 0.05, we can conclude that there is no
statistically significant difference in the satisfaction levels of men and women.
We will use the blue sig T-Test value in the Equal variances assumed row if Levene's Test
sig is greater than or equal to 0.05, indicating that the variance between the sexes is not
different.
+ With a sig T-Test value of 0.05, we can conclude that there is a statistically significant difference in
respondents' satisfaction levels between genders.
+ Because the sig T-Test value is greater than 0.05, we can conclude that there is no statistically
significant difference in the satisfaction levels of men and women.
Two sample T-test (Paired sample T-test): If the researchers want to compare two mean values from
two separate populations, each element in one population has a pairwise similarity relationship with
an element in the other. Giving each customer two products to try, the first and the one after the
28
improvement, and then asking them to rate each product is a simple example.
The goal is to see if the customer's review improves before and after the
product is improved. Use the Pair sample T test to accomplish this.
N Correlation Si
g.
,
Pair 1 00
1 Advertising & Sales 2 ,970 0
Paired Differences t df
Sig.
(2tailed)
Mean Std. Std. 95% Confidence Interval
Deviatio Error of the Difference
n Mean Lower Upper
-
29
III. Measuring association
+ Negative Correlation – occurs when the values of two variables move in opposite directions, such
that an increase or decrease in one variable is followed by a decrease or increase in the other
variable.
30
+ No Correlation – when the two variables have no linear dependence or relationship.
The researchers can use technology in their research project, including software like Excel and SPSS.
The following is the final result of the author's use of the analyze part of SPSS. This exemplifies the
dispersion of variables in particular.
In a research project, the author used SPSS to observe variable dispersion.
Correlation:
31
A correlation is a statistical measure of how closely two variables are related.
The measure works best with variables that have a linear relationship with one
another. A scatter plot can be used to visualize how well the data fits together. We can assess the
relationship between the variables and determine whether they are correlated or not using a scatter
plot.
Advertising Sales
1 ,
Pearson Correlation 970
**
Sig. (2-tailed) ,
Advertising 000
N 12 12
Pearson Correlation , 1
970
Sig. (2-tailed)
**
,
Sales 000
N 12 12
32
+ The closer r is to 1, the tighter the linear correlation. Moving closer to 1
indicates a positive correlation, while moving away from 1 indicates a
negative correlation. The linear correlation weakens as r approaches 0.
+ When represented on a scatter plot, r = 1 denotes absolute linear correlation. The points of
performance will be merged into a single line. + There is no linear correlation if r = 0. There will
be two scenarios at this point. For starters, there is no link between the two variables. Then
there's the fact that they have a nonlinear relationship.
Regression Analysis: A set of statistical methods for estimating relationships between a dependent
variable and one or more independent variables is known as regression analysis. It can be used to
determine the strength of a relationship between variables and to predict how they will interact
in the future.
To make regression analysis go as smoothly as possible, the author suggests using SPSS.
Variables Entered/Removeda
1 Advertisingb . Enter
a. Dependent Variable: Sales
Model Summaryb
Square Estimate
33
The adjusted R2 value of 0.936 indicates that the independent variable in the
regression affects 93.6 percent of the change in the dependent variable, with
out-of-model variables and random errors accounting for the remaining 6.4 percent. When the
Durbin – Watson coefficient = 0.778 is less than 1 and greater than 3, the researchers must pay close
attention because first-order series auto-correlation is very likely.
ANOVAa
Regression 8 7651440931,28
472613190,37 1 8
1 Residual 8 0 47261319,038
8124054121,66 1
Total
7 1
a. Dependent Variable: Sales
Sig = 0.00<0.05, There is a linear relationship between the independent variable and the dependent
variable
Coefficientsa
Model Unstandardized Standardi t Sig. Correlations Collinearity
Coefficients z ed Statistics
Coefficien
ts
B Std. Beta Zeroorde Partia Par Tolera VIF
Error r l t n ce
(Consta
388371, 12522,3 31,01 ,
nt)
6 14 99 4 000
1
Adverti 3,012 ,237 ,970 12,72 , ,970 ,970 , 1,000 1,00
34
si ng
4 000
970
0
a. Dependent Variable: Sales
1. Apply a range of statistical methods used in business planning for quality, inventory and
capacity management.
Probability distribution
Any random event's possible outcomes are determined by the probability distribution. It is also
defined as a set of possible outcomes of any random experiment based on the underlying sample
space. These parameters could be a set of real numbers, vectors, or any other entities. It's a part of
statistics and probability. The outcome of a random experiment is defined as an experiment whose
35
outcome cannot be predicted. Assume that when we toss a coin, we have no
way of knowing whether it will land on its head or tail. An outcome is the
possible outcome of a random experiment. A sample point is a collection of outcomes. we can always
create a probability pattern table in terms of variable and probabilities. (Probability Distributions in
Statistics (Definition & Examples), n.d.)
Consider the result of rolling two standard six-sided dice as a simple example of a probability
distribution. Each die has a 1/6 chance of rolling any single number from one to six, but when two
dice are added together, the probability distribution shown below is formed. The most common
result is seven (1+6, 6+1, 5+2, 2+5, 3+4, 4+3). On the other hand, two and twelve are far less likely
(1+1 and 6+6). (2020, Hayes)
(Source: Investopedia)
Normal distribution
Data is symmetrically distributed with no skew in a normal distribution. When plotted on a graph, the
data takes the shape of a bell, with the majority of values clustering around a central region and
tapering off as they move away from it. Because of their shape, normal distributions are also known
as Gaussian distributions or bell curves. The mean, median, and mode of a normal distribution are all
the same, and the distribution is symmetric about the mean, with half of the values falling below the
mean and the other half falling above the mean. The mean and standard deviation are two values
that can be used to describe the distribution. (Bhandari, 2021)
36
(Source: Scribbr)
The scale parameter is the standard deviation, while the mean is the location parameter. The mean
determines where the curve's peak is located. The curve moves right when the mean is increased,
and left when the mean is decreased. (Bhandari, 2021)
(Source: Scribbr)
The curve is stretched or squeezed by the standard deviation. A narrow curve is produced by a small
standard deviation, while a wide curve is produced by a large standard deviation. (Bhandari, 2021)
(Source: Scribbr)
37
Binomial probability distribution
The binomial distribution depicts the likelihood that x will succeed in n trials, with each trial having a
probability of success of p. + The binomial distribution's mean is np.
38
(Source: OnlineMathLearning)
A casino, for example, may offer a game in which players wager on the number of heads or tails in a
specific number of coin tosses. Let's say a player wagers $10 on six heads out of twenty coin tosses.
The binomial distribution is used by that player to calculate the probability of this happening.
The probability calculated is:
As a result, the chance of getting exactly six heads in twenty tosses is 0.037 percent.
Inference statistics
Statistical inference the procedure for analyzing and drawing conclusions from data that is subject to
random variation. Inferential statistics is another name for it. The statistical inference applications
include hypothesis testing and confidence intervals. Statistical inference is a method of using random
sampling to make decisions about a population's parameters. It aids in the evaluation of the
dependent and independent variables' relationship. The goal of statistical inference is to estimate the
uncertainty or variation from one sample to the next. It enables us to provide a likely range of values
for something in the population's true values. The following elements are used to make statistical
inferences:
+ Sample Size
+ Variability in the sample
39
To properly examine the data, inferential statistics is required. Proper data
analysis is required to interpret the research findings in order to reach an
accurate conclusion. It is primarily used to forecast the future for a variety of observations in various
fields. It assists us in drawing conclusions from the data. Statistical inference is used in a variety of
fields, including Business Analysis, Artificial Intelligence, Financial Analysis, Fraud Detection, Machine
Learning, Stock Market, and Pharmaceuticals.
2. Evaluate and justify the use of appropriate statistical methods supported by specific
organizational examples.
Regression is frequently used to determine how many specific factors influence the price movement
of an asset, such as commodity prices, interest rates, specific industries, or sectors. The author uses
regression as an appropriate statistical method for her specific organizational dataset in this research
project.
40
Based on above chart and table, In order to denote the amount of waste on advertising and sales in
twelve months last year on a marketing project, the author used the normal distribution. It clearly
shows how the value of advertising affects the value of sales. When the value of advertising rises, so
does the value of sales. The researcher, on the other hand, has made a comment about the sales-to-
advertising ratio. The author realized that Y- the value of a sale did not grow at the same rate as X-
the value of advertising behind the curtain. As a result, businesses spent too much money on
advertising and did not receive a fair return. To make the most of the budget, the company must
review its marketing strategy.
Levels of measurement
41
When the researchers discuss quantitative analysis and statistics, they are
almost certainly referring to the four horsemen of measurement: nominal,
ordinal, interval, and ratio.
On the Gradcoach website, Derek Jansen, a Master of Business Administration, has explained it
simply with plenty of practical examples. Derek Jasen has provided a specific definition for the type of
date used in quantitative analysis and statistics: “When collecting survey data (or, really, any kind of
quantitative data) for your research project, you'll come across two types of data: categorical and/or
numerical. These represent various levels of measurement. Data that reflects characteristics or
categories is referred to as categorical data (no surprise there!). Categorical data, for example, could
include variables like gender, hair color, ethnicity, coffee preference, and so on. To put it another
way, categorical data is a method of assigning numbers to qualitative data (e.g. 1 for male, 2 for
female, and so on).
Numerical data, on the other hand, refers to information that is inherently numerical and
quantitative. Age, height, and weight, for example. In other words, these are things that can be
measured numerically (i.e., they're quantitative). data that isn't categorical (which involves assigning
numbers to qualitative characteristics or groups). There are two levels of measurement within each
of these two main categories:
- Nominal and ordinal categorical data
- Interval and ratio data are numerical data.
Nominal: Nominal data is a type of categorical data that describes qualitative characteristics or
groups without regard for order or rank. Gender, ethnicity, eye color, and blood type are examples of
nominal data.
+ Owned refrigerator, car, or television brand
+ Favorite candidate for political office, shampoo, and meal
42
The data options in all of these examples are categorical, and there is no
ranking or natural order. In other words, they all have the same worth – none
of them are ranked higher than the others. As a result, the researchers can consider nominal data to
be the most fundamental level of measurement, reflecting categories without regard to rank or
order. (2020, Jansen)
Ordinal: Ordinal data takes things to the next level. It looks at categories in the same way that
nominal data does, but unlike nominal data, there is a meaningful order or rank between the options.
Consider the following examples of ordinal data:
+ Level of agreement (e.g., low, middle, high)
+ Income level (e.g., low, middle, high) (e.g. strongly disagree, disagree, neutral, agree, strongly
agree)
+ Political viewpoint (e.g. far left, left, centre, right, far right)
As can be seen in these examples, all of the options are still categories, but there is a difference in
how they are ordered or ranked. Although the researchers are unable to quantify the differences
between the options (because they are categories), they can order and/or logically rank them. As a
result, they can consider ordinal to be a slightly higher level of measurement than nominal. (2020,
Jansen)
Interval: Interval data are a type of numerical data, as we previously discussed. In other words, it's a
type of measurement that uses naturally quantitative data (is usually measured in numbers). Interval
data, in particular, has an order (similar to ordinal data) and the spaces between measurement points
are equal (unlike ordinal data). Doesn't it sound a little fluffy and abstract? Consider the following
examples of interval data:
+ Credit scores (300–850)
+ GMAT scores (200–800)
+ IQ scores
+ Fahrenheit temperature
Importantly, in all of these examples of interval data, the data points are numerical, Although the
data points are numerical, the zero point is chosen at random. A temperature of zero degrees
Fahrenheit, for example, does not imply that there is no temperature (or that there is no heat at all) –
it simply means that the temperature is ten degrees lower than the temperature of ten. Similarly, the
researchers will not be able to achieve a credit score of zero or a GMAT score of zero. Interval data, in
other words, is a numerical level of measurement that can measure the distance between points but
43
lacks a meaningful zero point – the zero is arbitrary. To summarize, interval-
type data provides a more sophisticated level of measurement than nominal
and ordinal data, but it is far from perfect. Ratio data, please. (Jansen, 2020)
Ratio: The most advanced level of measurement is ratio-type data. It is ordered/ranked, and the
numerical distance between points is consistent, just like interval data (and can be measured). The
fact that the zero point reflects an absolute zero (as opposed to interval data's arbitrary zero point)
makes it the king of measurement. In other words, a measurement of zero indicates that the variable
is not present. Here are some ratio data examples:
+ Weight, height, or length
+ Kelvin temperature (since zero Kelvin equals zero heat)
+ Time/duration (e.g. seconds, minutes, hours)
In all of these examples It demonstrates the absolute nature of the zero point. For instance, the term
"zero seconds" literally means "zero duration." Similarly, zero weight denotes the absence of weight.
It's not just a random number. Ratio-type data is the most advanced level of measurement because
of this.
Researchers can use ratio data to not only meaningfully measure distances between data points (i.e.
add and subtract), but also to meaningfully multiply and divide. 20 minutes, for example, is exactly
twice as long as 10 minutes. Credit scores (i.e. interval data) couldn't be used because there is no
such thing as a zero credit score. This is why, in the land of measurement levels, ratio data reigns
supreme. (Jansen, 2020)
Comparison of four levels of measurement
The levels of measurement in data – nominal, ordinal, interval, and ratio – are important to
understand because they directly influence which statistical techniques researchers can use in their
analysis. Each statistical test is limited to a specific set of data. Some techniques work with
categorical data (i.e. nominal or ordinal data), while others work with numerical data (i.e. interval or
ratio data), and still others work with a combination of the two. While statistical software such as
SPSS or R may "allow" the researchers to run the test with incorrect data, the results will be flawed at
best and meaningless at worst.
44
(Source: Questionpro)
The level of measurement shown in the previous figure is the ratio level, which is the most
sophisticated level of measurement. This type of level is used by researchers as a necessary dataset
in almost all studies. To better understand the differences between the levels of measurement, the
author suggests looking at the table below.
45
Data from cross-sections and time series
There are four different types of data. Cross sectional data, time series data,
repeated cross section data, and panel data are the four types of data. The author of this report
focuses on two common types of data: cross sectional data and time series data.
The main distinction between time series and cross sectional data is that time series data focuses on
a single variable over time, whereas cross sectional data focuses on multiple variables at the same
time. Furthermore, time series data are observations of a single subject at multiple time intervals,
whereas cross sectional data are observations of multiple subjects at the same time. (Lithmee, 2018)
Time series data
Time series data focuses on observations of a single person over time, usually at
regular intervals. It is the data of a single variable over time, such as months, quarters,
or years.
The time series data is represented by the letter Xt. The letter t stands for time. An
example of an organization's profit over a five-year period is shown below. Profit is a
variable that varies from year to year.
46
Usually, time series data is useful in business applications. Time measurement can be months,
quarters or years but it can also be any time interval. Generally, the time has uniform intervals.
Cross sectional data
There are several variables at the same time in cross sectional data. A cross sectional data set
includes maximum temperature, humidity, and wind speed for a few cities on a single day.
Max Temperature, Humidity, and Wind (all three behaviors) in New York City, SFO, Boston, and
Chicago(multiple entities) on 1/1/2015(single instance)
47
Discrete and continuous data
Andrew Zangre has updated his words about the definitions as well as
differences between discrete and continuous data: "Collect a set of round, defined numbers, and
they'll appear on the graph like the ones on the left." Individual and countable items are referred to
as discrete data (discrete variables). When measuring a data stream with a complex result range, the
results are displayed as a data range with a line (see: graphs on the right). Continuous data refers to
changes over time and encompasses concepts that aren't easily counted but necessitate precise
measurements (continuous variables). Disconnected, separate, and distinct are some synonyms for
discrete. These synonyms can be useful in learning more about discrete data.
Discrete data: We gather information in order to discover relationships, trends, and other concepts.
An underlying goal of tracking the number of push-ups you do each day for a month, for example, is
to
assess your progress and rate of improvement. As a result, your daily total is a distinct, isolated
number.
Because there is no definitive range for how many push-ups you can do in a day, the relationship
remains ambiguous. The more data you collect over time, the more insights you will be able to
derive.
some examples of discrete data one might gather:
Qualitative data can also be found in discrete data. The nationality you choose on a form is a discrete
piece of information. When you group the nationalities of everyone in your office, you can get
useful information for evaluating your hiring practices. Discrete data, both qualitative and
quantitative, make up the national census. We gain a better understanding of the population by
counting and collecting this identifying information. It assists us in making predictions while
recording history. This is a great example of the power of discrete data.
48
Continuous data: Continuous data refers to the unspecified number of
possible measurements between two realistic points. Because they're
usually gathered from precise measurements, these numbers aren't always as neat and tidy as
those in discrete data. Measuring a specific subject over time allows us to establish a defined
range within which we can reasonably expect to collect more data. It's all about accuracy when it
comes to continuous data. In these data sets, decimal points are frequently used, with the
number to the right stretched out as far as possible. For scientists, doctors, and manufacturers,
to name a few, this level of detail is critical. The following are some examples of continuous data:
+ The weight of newborn babies
+ The daily wind speed
Data presentation
The presentation of data is crucial in any research project. Every hypothesis is put to the test using a
dataset. Data has a significant impact on the final outcome of any study. Numerical and graphical data
presentation are the two types of data presentation.
Numerical presentation
There are many different ways to present data numerically, including arranging it in ascending or
descending order, and categorizing it in tabular form.
Graphical presentation
A method of analyzing numerical data is to use graphical presentation. In a diagram, it depicts the
relationship between data, ideas, information, and concepts. It is simple to comprehend and one of
the most important learning techniques. It is always dependent on the type of data in a given
domain. Graphical representations come in a variety of shapes and sizes. The following are a few of
them: Graph in line: A line graph, also known as a linear graph, is a type of graph that is used to
display continuous data and is useful for forecasting future events over time. A graph depicting the
differences in frequencies or percentages among interval-ratio variable categories. Each category's
49
frequencies are represented by points that are placed above the category's
midpoint and connected by a straight line.
Bar graph: The data is compared using solid bars to represent the quantities in a bar graph, which is
used to display the category of data. A graph depicting the differences in frequencies or percentages
among nominal or ordinal variable categories. The categories are represented as rectangles of equal
width with a height proportional to their frequency or percentage.
Circle graph: Also known as a pie chart, this diagram depicts the relationships between the various
components of a whole. The circle is 100 percent filled, and the occupied categories are represented
by specific percentages such as 15%, 56 percent, and so on. A pie chart depicts the differences in
frequencies or percentages among nominal or ordinal variable categories.
Scatter diagram: We can determine the nature of the relationship between the variables using a
scatter diagram or a dot chart. Each axis represents a quantitative measure, and each dot represents
a single piece of data. The relationship between the two variables is weaker if the plotted points are
widely scattered.
Box plot: A box and whisker plot is a method of abstracting a set of data that is estimated using an
interval scale. It's also known as a box plot. These are primarily used to interpret data. It's a type of
graphical method that shows how the data in a dataset changes over time. The data can also be
displayed using a histogram. However, a histogram is sufficient as a display. A box and whisker plot is
50
preferable to a histogram because it allows multiple sets of data to be displayed
in the same graph, providing more information. People use box plots or
graphical representations to figure out what's going on. Variability, central value, and distribution
shape
When the researchers use a graph to create a box plot, they draw a box from the first to the third
quartile. The median is a vertical line that runs through the middle of the box. Each quartile's
whiskers (small lines) lead to the minimum or maximum value.
Line plot: A line plot is a graph that depicts the frequency with which data appears along a number
line. On a given number line, it displays the frequency of data. When that data appears again, an'x'is
placed above a number line. When comparing fewer than 25 different numbers, line plots provide a
quick and easy way to organize data.
3. Critically evaluate the use of different types of charts and tables for communicating given
variables.
Advantages and Disadvantages among the chart
Bar chart Bar graphs are used to compare + A bar graph + The bar graph may
items across groups or to track summarizes a large set fail to reveal patterns,
changes over time. Bar graphs, on of data in a simple causes, and effects in
the other hand, are best for visual format some cases.
estimating change over time when + It displays each + It is easily
the changes are larger. category of data in a manipulated to
frequency distribution produce false data.
+ It clarifies data
trends better than a
table
+ It aids in estimating
key values at a glance.
Line chart A line graph is a graph that depicts + The best way to + Only works for data
51
changes over time using points and visualize changes
lines. It's a graph that shows a line + Good for showing
connecting several points or a line trends over time that is updated on a
that depicts the relationship + Good for showing regular basis
between the points, to put it relationships with + When comparing
another way. The diagram depicts continuous periodical more than seven
quantitative data between two data categories, it's easy to
changing variables by using a make things look a
straight line or curve to connect a little jumbled.
series of successive data points.
Histogram A histogram is a diagram made up + It allows viewers to a frequency histogram,
of rectangles whose area is easily compare data, it is extremely difficult,
proportional to the frequency of a and it also works well if not impossible, to
variable and whose width is equal with large amounts of extract the exact
to the class interval. data amount of "input."
+ It provides a more
concrete level of
consistency, as the
intervals are always
equal, allowing for
easy data transfer
from frequency tables
to histograms.
Pie chart The data in a circular graph is + A straightforward + A pie chart becomes
represented by a pie chart, which and easy-to- less effective when too
is a type of graph. The pie slices understand many pieces of data
represent the data's relative size. illustration. It visually are used. If there are
It's a type of pictorial data represents data as a too many pieces of
representation. In order to create a fraction of a whole, data, they may
pie chart, you'll need a list of which can be an become crowded and
categorical and numerical effective difficult to read, and
variables. The term "pie" refers to communication tool even adding data
52
the whole, while "slices" refers to for even the most
the individual parts of the pie. inexperienced
audience. labels and numbers
+ It allows the may not help.
audience to see a data
comparison at a + Because this chart
glance, allowing them only represents one
to perform an data set, you'll need a
immediate analysis or series to compare
quickly comprehend multiple sets. This may
information. make it more difficult
+ The use of this chart for readers to analyze
eliminates the need and assimilate
for readers to examine information quickly.
or measure underlying
numbers. You can + Because the reader
manipulate data in the must account for
pie chart to emphasize angles and compare
points you want to slices that are not
make. adjacent, it has its
problems in comparing
the data slices.
Scatter plot Scatterplots aren't commonly used Clearly shows data It's impossible to label
in infographics, but they do have correlation (shows data points, and
their place. They can display large positive, negative, finding exact values is
amounts of data and make it strong, and weak difficult; error bars and
simple to see correlations and relationships); method too many data points
clustering effects between of illustration non- can quickly make a
variables. Scatterplots are linear patterns; shows graph unreadable; and
extremely useful as a quick data spread and you can't show a
53
overview and analytical tool, and outliers; clearly shows
they can be used with almost any atypical relationships;
continuous scale data. used for data relationship between
extrapolation and more than two
interpolation. variables at the same
time.
Box plot It is a standardized method of + It's a good way to + The original data is
displaying data distributions based summarize a lot of not clearly displayed in
on the dataset's minimum, first information the box plot
quartile, median, third quartile, + It shows the range + The mean and mode
and maximum. and distribution of cannot be determined
data on a number line using a box plot
+ It highlights outliers + It can only be used
with numerical data
54
Level of Type of data Description Graph
measurement
Example
Nominal Discrete Items can only be put Bar graph Dichotomous
in groups. Numerical
Pie chart + Yes/No
comparisons are
+ Male/Female
impossible
Type/Category
+ Shape
+ Color
Ordinal/Rank Discrete Items can be Bar graph Quality rankings,
categorized and reference rankings,
Pie chart
ordered in higher or market position,
Stem and leaf
lower format, but social class
numerical difference
cannot be calculated
Interval Continuous Numerical difference All tools for Temperature,
between values is continuous attitude options,
meaningful but ratio data feeling, though
cannot be calculated
Ratio Continuous Ratios between two All tools for Age, weight, length,
values are continuous sales, income, costs
meaningful data
With the current state of strong economic growth, a large number of businesses have been
established. As a result, the companies find themselves in a fierce battle for market share. As a result,
every business recognizes the importance of marketing, particularly digital marketing. This
necessitates marketing employees having a thorough understanding of nearly all current techniques
as well as professional working skills.
55
In terms of marketing, datasets that are intended to approach customers are
extremely important, so researchers must understand how to effectively
analyze and use data as well as collected information. The author of this report has emphasized the
importance of data analysis by conducting a marketing research project, which used a dataset from
the previous year's company, as well as the above-mentioned results of marketing effectiveness
analysis. The author has realized that this business has yet to receive the deserved return on its
investment. Perhaps, in some cases, marketing researchers should use more methods and techniques
analysis, according to the author. Using various graph presentations to see surface fluctuations
among internal and external elements, which have a significant impact on enterprise performance.
Researchers may also use Excel, R, or SPSS software to examine the correlation and the significance
of mutual interactions.
When researchers do their best to make the most of analyzed data in their market analysis, the
company is more likely to perform well. However, keep in mind that the best way to achieve
beautiful organizational behavior is to combine rational data with appropriate strategy.
Conclusion
Data is the foundation of everything; without it, there is no information, and without it, no knowledge
or wisdom can be formed. Human beings are truly mature when they understand how to effectively
use data. People use data in a variety of ways, including business, education, and everyday life. It's a
long process from data collection to data analysis, and the end result is the process's success. Data is
extremely useful when conducting hypothesis research, and data analysis is an important part of
determining a hypothesis. Every researcher should be able to analyze a dataset efficiently in order to
achieve a good end result.
Reference list:
- Bhandari, P., 2021. Normal Distribution | Examples, Formulas, & Uses. [online] Scribbr.
Available at: <https://www.scribbr.com/statistics/normal-distribution/>
[Accessed 23 June 2021].
56
- www.onlinemathlearning.com. n.d. Binomial Distribution (examples,
solutions, formulas, videos). [online] Available at:
<https://www.onlinemathlearning.com/binomial-distribution.html> [Accessed 23 June 2021].
- QuestionPro. n.d. Nominal, Ordinal, Interval, Ratio Scales with Examples | QuestionPro.
[online] Available at: <https://www.questionpro.com/blog/nominal-ordinal-interval-ratio/>
[Accessed 23 June 2021].
- Lithmee, 2018. Difference Between Time Series and Cross Sectional Data | Compare the
Difference Between Similar Terms. [online] Compare the Difference Between Similar Terms.
Available at: <https://www.differencebetween.com/difference-between-time-series-and-
cross-sectionaldata/> [Accessed 23 June 2021].
- Zangre, A., 2019. [online] Available at: <https://www.g2.com/articles/discrete-vs-
continuousdata> [Accessed 23 June 2021].
- Zach, V., 2018. Measures of Central Tendency: Definition & Examples - Statology. [online]
Statology. Available at: <https://www.statology.org/measures-central-tendency/> [Accessed
15 June 2021].
- Frost, J., 2021. [online] Available at: <https://statisticsbyjim.com/basics/variability-
rangeinterquartile-variance-standard-deviation/> [Accessed 18 June 2021].
- Anderson, S., 2021. Learn How Standard Deviation Is Determined by Using Variance. [online]
Investopedia. Available at: <https://www.investopedia.com/ask/answers/021215/what-
differencebetween-standard-deviation-and-variance.asp> [Accessed 19 June 2021].
- S, S., 2017. Difference Between Population and Sample (with Comparison Chart) - Key
Differences. [online] Key Differences. Available at: <https://keydifferences.com/difference-
between-populationand-sample.html> [Accessed 20 June 2021].
- McCombes, S., 2019. Sampling Methods | Types and Techniques Explained. [online] Scribbr.
57
- Hayes, A., 2020. What Are the Odds? How Probability Distribution Works.
[online] Investopedia. Available at:
<https://www.investopedia.com/terms/p/probabilitydistribution.asp> [Accessed 23 June
2021].
58