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STAT1510 EXAM PACK SEPTEMBER 2023 COMPLETE WITH ANSWERS
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- University Of South Africa
STAT1510 EXAM PACK SEPTEMBER 2023 COMPLETE WITH ANSWERS
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1STA1510 NOTES AND MEMOS
STUDY UNIT 1
Key questions for this unit
What is Statistics?
What is the difference between Population and a Sample?
What is the difference between a parameter and a Statistic?
Distinguish between Qualitative and Quantitative variables.
Distinguish between Nominal and Ordinal variables.
Distinguish between Discrete and Continuous variables.
Distinguish between Scale and Ratio variables.
DEFINITIONS
Statistics is a way to get information from data. In other words, statistics is a tool ‘’like a
toolbox’’ used to extract information form collected data. Statistics has two main branches;
Descriptive and Inferential statistics.
Descriptive statistics: This deals with methods of organising, summarizing and presenting
data in a convenient and informative way. In descriptive statistics, we use graphs, tables,
numerical measures like mean, range, median mode etc to summarise data.
Inferential statistics: This is a body of methods used to draw conclusions or inferences about
characteristics of population based on sample data.
A population: This is the group of all items of interest to a statistics practitioner. It could
be people, cars, house etc. It is frequently very large and may, in fact, be infinitely large.
A sample: This is a set of data drawn from the studied population. In other words, a sample
is part of a population.
A parameter: Any descriptive measure of a population is a parameter. Examples of
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parameters include; population size (N ) , population variance ( sigma-squared σ ),
,population standard deviation (sigmaσ ). In other words, any numerical summary from a
population is a parameter.
A statistic: Any descriptive measure of a sample is a statistic. Examples include; sample
size (n) , sample variance ( s2 ), sample standard deviation ( s ). In other words, any
numerical summary from a sample is a statistic.
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TYPES OF VARIABLES
1.1 Introduction to this study unit
This unit introduces the concepts of types of variables. There are basically
two types of variables in statistics; Qualitative (think in terms of quality of
life) and Quantitative (if you quantify something you could count it).
Qualitative variables are then classified into nominal and ordinal variables.
Quantitative variable can be classified into discrete and continuous
variables. Once you know your variable is quantitative, it helps to ask
yourself if you have actually counted (then discrete) or measured (then
continuous), when you gather the values.
The diagram below is a mind map of what we shall focus on in this section.
Please note that though we have to know how to differentiate between
variables, questions in this section are set in application form as we shall see
when we get to examples and exercises.
1.2 Qualitative Vs Quantitative variables
1.2.1 Qualitative Variables (Categorical Variable)
Also known as categorical variables, qualitative variables are variables with no natural sense
of ordering. They are therefore measured on a nominal scale. For instance, hair colour
(Black, Brown, Gray, Red, Yellow) is a qualitative variable, as is name (Adam, Becky,
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Christina, Dave . . .). Qualitative variables can be coded to appear numeric but their
numbers are meaningless, as in male=1, female=2. Variables that are not qualitative are
known as quantitative variables.
1.2.2 Quantitative Variables
Quantitative variables are variables measured on a numeric scale. Height, weight, response
time, subjective rating of pain, temperature, and score on an exam are all examples of
quantitative variables. Quantitative variables are distinguished from categorical (sometimes
called qualitative) variables such as colour, religion, city of birth, sport in which there is no
ordering or measuring involved.
1.3 Nominal Vs Ordinal variables
1.3.1 Nominal Variables
A nominal variable has values which have no numerical value. As a result the order or
sequence of nominal variables is not prescribed. Examples of nominal variables are
gender, occupation.
1.3.2 Ordinal variables
An ordinal variable is similar to a categorical variable. The difference between the two is
that there is a clear ordering of the variables. For example, suppose you have a variable,
economic status, with three categories (low, medium and high). In addition to being able to
classify people into these three categories, you can order the categories as low, medium
and high.
Please note that the major difference between ordinal and nominal is that order is
considered to be important in ordinal variables than in nominal variables.
1.4 Discrete Vs Continuous variables
1.4.1 Discrete variables
Variables that can only take on a finite number of values are called "discrete variables." Or A
variable that takes values from a finite or countable set, such as the number of legs of an
animal. All qualitative variables are discrete. Some quantitative variables are discrete, such
as performance rated as 1,2,3,4, or 5, or temperature rounded to the nearest degree.
1.4.2 Continuous variables
A continuous variable is one for which, within the limits the variable ranges, any value is
possible. For example, the variable "Time to solve a mathematical problem" is continuous
since it could take 2 minutes, 2.13 minutes etc. to finish a problem.
I like telling my students to look at discrete variables as countable variables with gaps in
between say the number of students in a discussion class, and to look at continuous
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