Lu2 introduction to statistics

QUANTITATIVE TECHNIQUES
5112
felixmaboko83@gmail.com
Lecturer: Mr Felix Maluleke

Chapter 1:
Introduction to Statistics

What is Statistics?
Statistics is therefore defined as a set of mathematically based and techniques to transform raw
(unprocessed) data into a few summary measures that represent useful and usable information
to support effective decision making.
Information
To make sound business decision, a manager needs high-quality information. Information must
be timely, accurate, relevant, adequate and easily accessible. However, information to support
decision making is seldom readily available in the format, quality and quantity required by the
decision maker. More often than not, it needs to be generated from data.
Data
What is more readily available – from a variety of sources and of varying quality and quantity –
is data. Data consists of individual values that each conveys little useful and usable information
to management. Three examples of data are: the purchase value of a single transaction at a
supermarket (e.g. R214); the time it takes a worker to assemble a single part (e.g. 7.35 minutes).

The Language of Statistics
A random variable
Is any attribute of interest on which data is collected and analysed.
Data
Data is the actual values (numbers) or outcomes recorded on a random variable. Examples:
• the brand of coffee preferred (data: Nescafe, Ricoffy, Frisco).
• the daily occupancy rates of hotels in Cape Town (data: 45%, 72%, 54%)

Terms and Concepts of Statistics
Sampling Unit
A sampling unit is the object being measured, counted or observed with respect to
the random variable under study. Examples: Consumer, an employee, a household,
a company or a product.
More than one random variable can be defined for a given sampling unit. Example:
an employee could be measured in terms of age, qualification and gender.
Population
A population is the collection of all possible data values that exist for the random
variable under study. Example:
• For a study on hotel occupancy levels (the random variable) in Cape Town only.
All hotels in Cape Town would represent the target population.
• To research the age, gender, and savings levels of banking clients (three random
variables being studied), the population would be all savings account holders and
all banks.

Terms and Concepts of Statistics
Population Parameter
A population parameter is a measure that describes a characteristic of a population.
A population average is a parameter, so is a population proportion. It is called a
parameter if it uses all the population data values to compute its value.
Sample
A sample is a sub set of data values drawn from a population. Samples are used
because it is often not possible to record every data values of the population,
mainly because of cost, time and possible item destruction. Example: a sample of 25
hotels in Cape Town is selected to study hotel occupancy levels.
Sample Statistics
A sample statistic is a measure that describes a characteristic of a sample. The
sample average and a sample proportion are two typical sample statistics. Example:
appropriate sample statistics are: the average hotel occupancy level for the sample
of 25 hotels surveyed.

Symbols used to describe statistical concepts
Statistical terms and symbols to distinguish a sample statistics
from a population parameter for a given statistical measure.
Statistical measure Sample statistics Population parameter
Mean 𝑥 µ
Standard deviation S 𝜎
Variance 𝑆2
𝜎2
Size n N
Proportion 𝜌 𝜋
Correlation r 𝜌

Components of Statistics
Descriptive Statistics
Descriptive statistics condense sample data into a few summary descriptive
measures (only describes the behaviour of a random variable in a sample).
Descriptive statistics organise, summarise and extract essential information
contained within the data for communication to management. These allows users to
identify profiles, patterns, relationships, and trends within the data.
Inferential Statistics
Inferential statistics generalises sample findings to the broader population.
Inferential statistics is that area of statistics that allows managers to understand the
bigger population picture of a random variable based on the sample evidence.
Statistical Modelling
Statistical modelling constructs equations between variables that are related to
each other. These equations (called models) are used to estimate or predict values
of one of these variables based on values of related variables.

Data Types and Measurement Scales
Qualitative random variables
Qualitative random variables generate categorical (non-numeric) response data.
The data is represented by categories only. Examples: the gender of a consumer is
either male or female; an employee’s highest qualification is either a matric, a
diploma or a degree.
Quantitative random variables
Quantitative random variables generate numeric response data. These are real
numbers that can be manipulated using arithmetic operations (add, subtract,
multiply and divide). Examples: the age of an employee (e.g. 46 years, 28 years; 32
years); the price of a product in different stores (e.g. R6.75; R7.45; R7.20; R6.99)
Numeric data can be further classified as either discrete or continuous.

Types of Numeric Data
Discrete data
Discrete data is whole number (or integer) data.
Examples: the number of students in a class (e.g. 24;37;41;46), the number of cars
sold by a dealer in a month (e.g. 14;27;21;16), and the number of machine
breakdowns in a shift (e.g. 4;0;6;2).
Continuous data
Continuous data is any number that can occur in an interval data.
Example: the assembly time for a part can be between 27 minutes and 31 minutes
(e.g. assembly time = 28.4 min), a passenger’s hand luggage can have a mass
between 0.5 kg and 10 kg (e.g. 2.4 kg) and the volume of fuel in a car tank can be
between 0 litres and 55 litres (e.g. 42.38 litres).

Measurement of Scale
Nominal data
There must be distinct classes but theses classes have no quantitative properties.
Therefore, no comparison can be made in terms of one category being higher than
the other. Examples of nominal-scaled categorical data are:
• Gender (1 = male; 2 = female)
• City of residence (1 = Pretoria; 2 = Durban; 3 = Cape Town; 4 = Bloemfontein)
• Home language (1 = Xhosa; 2 = Zulu; 3 = English; 4 = Afrikaans; 5 = Sotho)
There are no quantitative properties for this variable or these classes and,
therefore, gender is a normal variable.
Measurement is the process of assigning numbers or labels to objects, person, or
events in accordance with specific rules to represent quantities or qualities of
attributes.
• We do not measure specific objects, persons, etc., we measure attributes or
features that define them.
Different types of Data

Ordinal data
There are distinct classes but these classes have a natural ordering or ranking. The
difference can be ordered on the basis of magnitude. Examples of ordinal-scaled
categorical data are:
• Size of clothing (1 = small; 2 = medium; 3 = large; 4 = extra large)
• Product usage level (1 = light; 2 = moderate; 3 = heavy;)
• Response to a survey question: ‘Rank your top three TV programmes in order of preference’
(1 = first choice; 2 = second choice; 3 = third choice).
• Final position of horses in a race is an ordinal variable. The horses finish first, second, third,
fourth, and so on.
The different between first and second is not necessarily equivalent to the
difference between second and third, or between third and fourth.

Interval data
It is possible to compare differences in magnitude, but importantly the zero point does not have a
natural meaning. It captures the properties of nominal and ordinal data – used by most psychological
tests. Examples of rating scales responses are shown in the table below. Statements 1,2 and 3 are
illustrations of semantic differential rating scales that use bipolar adjectives (e.g. very slow to
extremely fast service), while statement 4 illustrates a likert rating scale that uses a scale that
ranges from strongly disagree to strongly agree with respect to a statement or an opinion.
1. How would you rate your chances of promotion after the next performance appraisal?
Very poor
1
Poor
2
Unsure
3
Good
4
Very good
5
2. How satisfied are you with your current job description?
Very dissatisfied
1
Dissatisfied
2
Satisfied
3
Very satisfied
4
3. What is your opinion of the latest Idols TV series?
Very boring
1
Dull
2
Ok
3
Exciting
4
Fantastic
5
4. The performance appraisal system is biased in favour of technically oriented employees.
Strongly disagree
1
Disagree
2
Unsure
3
Agree
4
Strongly agree
5
interval data possesses the
two properties of rank-
order (same as ordinal data)
and distance in terms of
how much more or how
much less an object
possesses of a given
characteristic. However, it
has a no zero point.
Therefore it is not
meaningful to compare the
ratio of interval scaled
values with one another.
Example, we can’t conclude
that a rating of 4 is twice
important as a rating of 2.

Ratio data
• It is the highest level of measurement
• This level has all the three attributes:
o magnitude
o Equal interval
o Absolute zero point
• It represent continuous values
Examples of ratio-scaled data are: employee ages (years), customer income (R), distance
travelled (km), door height (cm), product mass (g), volume of liquid in a container (ml),
machine speed (rpm), tyre pressure (psi), product price (R), length of service (months)
and number of shopping trips per month (0; 1; 2; 4; etc).

Different Sources of Data
Internal data source
Internal data source in a business context, is data sourced from within a company. It is
data generated during the normal course of business activities.
It is relatively inexpensive to gather, readily available from company databases and
potentially of good quality (since it is recorded using internal business systems).
Examples of internal data sources are:
• Sales vouchers, credit notes, accounts receivable, accounts payable and asset registers for
financial data
• Production cost records, stock sheets and downtime records for production data
• Time sheets, wages and salaries schedules and absenteeism records for human resource data
• Product sales records and advertising expenditure budgets for marketing data.

Different sources of Data
External data source
external data source in a business context, is data that exist outside an organisation.
They are mainly business associations, government agencies, universities and various
research institutions.
The cost and reliability of external data is dependent on the source. A wide selection of
external databases exist and, in many cases, can be accessed via the internet, either free
of charge or for a fee.
A few examples of relevant to managers are:
• Statistics South Africa – for macroeconomic data
• South African Chamber of Business – for trade surveys,
• I-Net Bridge and etc.

Different sources of Data
Primary data source
Primary data is data that is recorded for the first time at source and with specific
purpose in mind. Primary data can be either internal (if it is recorded directly from an
internal business process, such as machine speed settings, sales invoices, stock sheets
and employee attendance records) or external (e.g. obtained through surveys such as
human resources surveys, economic surveys and consumer surveys (market research)).
Advantage of primary sourced data
It is its high quality (i.e. relevancy and accuracy). This is due to

Lu2 introduction to statistics

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