Class notes
lecture notes
- Course
- Statistics (STAT181)
- Institution
- Walter Sisulu University (WSU)
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1Chapter 1 – Terminology
1.1 Definitions
Data/Data set – Set of values collected or obtained when gathering information on some
issue of interest.
Examples
1 The monthly sales of a certain vehicle collected over a period.
2 The number of passengers using a certain airline on various routes.
3 Rating (on a scale from 1 to 5) of a new product by customers.
4 The yields of a certain crop obtained after applying different types of fertilizer.
Statistics – Collection of methods for planning experiments, obtaining data, and then
organizing, summarizing, presenting, analyzing, interpreting the data and drawing
conclusions from it.
Statistics in the above sense refers to the methodology used in drawing meaningful
information from a data set. This use of the term should not be confused with statistics
(referring to a set of numerical values) or statistics (referring to measures of description
obtained from a data set).
Descriptive Statistics – Collection, organization, summarization and presentation of data.
To be discussed in chapter 2.
Population – All subjects possessing a common characteristic that is being studied.
Examples
1 The population of people inhabiting a certain country.
2 The collection of all cars of a certain type manufactured during a particular month.
3 All patients in a certain area suffering from AIDS.
4 Exam marks obtained by all students studying a certain statistics course.
Census – A study where every member (element) of the population is included.
Examples
1 Study of the entire population carried out by the government every 10 years.
2 Special investigations e.g. tax study commissioned by a government.
, 2
3 Any study of all the individuals/elements in a population.
A census is usually very costly and time consuming. It is therefore not carried out very often.
A study of a population is usually confined to a subgroup of the population.
Sample – A subgroup or subset of the population.
The number of values in the sample (sample size) is denoted by n.
The number of values in the population (population size) is denoted by N.
Statistical Inference – Generalizing from samples to populations and expressing the
conclusions in the language of probability (chance). To be discussed in chapters 5-9.
Variable – Characteristic or attribute that can assume different values
Discrete variables – Variables which can assume a finite or countable number of possible
values. Such variables are usually obtained by counting.
Examples
1 The number of cars parked in a parking lot.
2 The number of students attending a statistics lecture.
3 A person’s response (agree, not agree) to a statement. A one (1) is recorded when the
person agrees with the statement, a zero (0) is recorded when a person does not agree.
Continuous variables – Variables which can assume an infinite number of possible values.
Such variables are usually obtained by measurement.
1 The body temperature of a person.
2 The weight of a person.
3 The height of a tree.
4 The contents of a bottle of cool drink.
Measurement scales
Qualitative variables – Variables which assume non-numerical values.
Examples
1 The course of study at university (B.Com, B.Eng , BA etc.)
2 The grade (A, B, C, D or E) obtained in an examination.
, 3
Nominal scale – Level of measurement which classifies data into categories in which no
order or ranking can be imposed on the data.
A variable can be treated as nominal when its values represent categories with no intrinsic
ranking. For example, the department of the company in which an employee works.
Examples of nominal variables include region, postal code, or religious affiliation.
Ordinal scale – Level of measurement which classifies data into categories that can be
ordered or ranked. Differences between the ranks do not exist.
A variable can be treated as ordinal when its values represent categories with some intrinsic
order or ranking.
Examples
1 Levels of service satisfaction from very dissatisfied to very satisfied.
2 Attitude scores representing degree of satisfaction or confidence and preference rating
scores (low, medium or high).
3 Likert scale responses to statements (strongly agree, agree, neutral, disagree, strongly
disagree).
Quantitative variables – Variables which assume numerical values.
Examples
Discrete and continuous variables examples given above.
Interval scale – Level of measurement which classifies data that can be ordered and ranked
and where differences are meaningful. However, there is no meaningful zero and ratios are
meaningless.
Examples
1 The difference between a temperature of 100 degrees and 90 degrees is the same
difference as that between 90 degrees and 80 degrees. Taking ratios in such a case does not
make sense.
2 When referring to dates (years) or temperatures measured (degrees Fahrenheit or Celsius)
there is no natural zero point.
Ratio scale – Level of measurement where differences and ratios are meaningful and there is
a natural zero. This is the “highest” level of measurement in terms of possible operations that
can be performed on the data.
, 4
Examples
Variables like height, weight, mark (in test) and speed are ratio variables. These variables
have a natural zero and ratios make sense when doing calculations e.g. a weight of 80
kilograms is twice as heavy as one of 40 kilograms.
Summary of 4 measurement scales
Measurement scale examples Meaningful calculations
Nominal Types of music Put into categories
University faculties
Vehicle makes
Ordinal Motion picture ratings: Put into categories
G- General audiences Put into order
PG-Parental guidance
PG-13 – Parents cautioned
R - Restricted
NC 17 – No under 17
Interval Years: 2009,2010, 2011 Put into categories
Months: 1,2, . . . , 12 Put into order
Find differences between values
Ratio rainfall Put into categories
humidity Put into order
income Find differences between values
Find ratios
Experiment – The process of observing some phenomenon that occurs.
An experiment can be observational or designed.
1 A designed experiment can be controlled to a certain extent by the experimenter.
Consider a study of 4 fuel additives on the reduction in oxides of nitrogen. You may have 4
drivers and 4 cars at your disposal. You are not particularly interested in any effects of
particular cars or drivers on the resultant oxide reduction. However, you do not want the
results for the fuel additives to be influenced by the driver or car. An appropriate design of
the experiment (way of performing the experiment) will allow you to estimate effects of all
factors of interest without these outside factors influencing the results.
2 An observational study is not controlled by the experimenter. The characteristic of interest
is simply observed and the results recorded. Examples are
2.1 Collecting data that compares reckless driving of female and male drivers.
2.2 Collecting data on smoking and lung cancer.
Parameter – Characteristic or measure of description obtained from a population.
Examples
1 Mean age of all employees working at a certain company.
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