Introduction to Mathematics
for Business Studies
Lecture 1
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Assessment
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Credit value is three.
30% comes from your test.
40 % comes from your final exam to be
held sometimes in mid may next year.
Recommended Text book :
• Introduction to Business Statistics
 Ronald M.Weirs
Your attendance is important.
15 % comes from tutorial participation.
15 % comes from assignment.
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Structure of your lecture
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The first few minutes will be spent on doa
recital.
Objectives
The next 50 minutes or so is your main
lecture
The last few minutes shall be recapitulation.
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Note
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You will not be asked simple definitions or
descriptions of concepts or ideas in your
test or examination.
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Rather, your understanding of the lessons
delivered and your ability to apply theories
or concepts.
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Objectives
• look at different forms of raw data
• differentiate between continuous and
discrete data
• define terms and concepts in statistics
• explain methods used in data collection
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What is Statistics?
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Statistics can be regarded as the scientific
method of collecting, arranging, analysing
and interpreting numerical data so that
conclusions (makes inferences) from the
information are obtained.
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Levels or scales of data
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Nominal Scale
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Ordinal Scale
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Interval Scale
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Ratio Scale
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Nominal Scale
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This is the simplest scale, consists of only
names, labels and categories.
It uses numbers to indicate how much
data there are in a particular category
E.g.
Toyota Cars
22%
Mitusibishi Cars
28%
Nissan Cars
12%
Any
numbers used to code the
observation cannot be used in statistical
calculations.
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Ordinal Scale
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Ordinal data is data that can be ranked or
arranged in some order.
For example, ‘1st, 2nd and 3rd’ or ‘good,
better and best’.
Again, any numbers assigned to such data
should not be used in calculations.
For example, if we assign (say) 1= agree,
2 = disagree and 3 = no opinion, it would
be meaningless to calculate their average
or the difference between them.
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The Interval Scale
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It has all the characteristics of the ordinal
scale.
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Unlike the ordinal scale the unit of
measurement allows us to describe how
much more or less one object possesses
than another.
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There is no absolute zero level.
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The Ratio Scale
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The ratio scale is similar to the interval
scale, but has an absolute zero and ratio
of any two values is meaningful. For e.g. if
you have $0, you have no money. If you
have $100 and your sister has $50, then
you have twice as much as your sister.
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Examples include weights,
money, election votes .
distances,
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Two main areas of Statistics
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Descriptive statistics
• Consists of methods of organizing, displaying
and describing data by using tables, graphs and
summary measures.
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Inferential statistics
• Consists of methods that use sample results to
help make decisions or predictions about a
population.
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Inferential Statistics
• Statistical inductive reasoning
 From small to large approach. You use a
sample of data taken from a population
to make a statement about the
population.
 E.g., confidence intervals, estimation of
the mean.
• Statistical deductive reasoning
 From large to small approach. You use a
population to make a statement about a
sample taken from the population
 E.g., probabilities
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Uses of statistics
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To study the trend and pattern of sets of
data.
Evaluation.
Comparing various sets of data.
Planning ,e.g. how many branches to be
set up.
Forecasting, e.g. how much sales
expected in the second quarter ?
And eventually for making decision.
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Statistical data
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Quantitative
• Basically they are arithmetical values.
 It can be continuous e.g. weights or heights
of students
 It can be discrete e.g. the number of
students in this class
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Qualitative data
• They are non arithmetical values e.g. students
behaviors (lazy, very lazy, extremely lazy)
• If they are numerically coded, they are still
qualitative value. (e.g.1 = Chinese, 2 = malay,
3 = Indian)
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Some concepts used in statistics
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Variable
Population
Sample
Parameter
Sample statistic
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Variable
• A variable is a characteristic of data that
we want to study and examine.
• It can either be continuous or discrete.
• Continuous variables can take any
values within a specified range. E.g.
temperature , height of students.
• Discrete variables can only take exact
values. E.g. the number of shoppers
visited a shop in a day.
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Population
• Population is a group or a set of data
that we are trying to study and about
which we want to make decisions or
conclusions.
• It can either be finite or infinite.
• E.g. of finite population , just like
discrete variable, is the number of cars
in the Tutong district.
• E.g. of infinite population, is student’s
weights.
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Sample
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A sample is a portion or subset of the
population selected for study.
The characteristic of the sample will then
be used to estimate the nature of the
same characteristic of the population.
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Parameter
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A parameter is a numerical measure
used
to
describe
an
entire
population.
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The value is a fixed constant.
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E.g. the average height of Bruneians.
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Sample statistic
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The sample statistic is a numerical
measure used to describe a sample.
The value of statistic will usually vary
from sample to sample.
E.g. the average height of BP
students ( a sample ) which is used
to estimate the height of all
Brunieans.
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Methods of collecting data
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Direct observation
Personal interview
Telephone interview
Mailed questionnaires
Abstract from published statistics
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Direct observation
• This method requires sending out a
person to record exactly what is
happening. It has the advantage in that
it reduces the chance of recording
incorrect data. This method is expensive
and not economical to be used
especially when we have a large data.
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Personal interview
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This requires sending interviewers asking
people a set of questions.
It has the advantage in that any dispute
or misunderstanding can be resolved on
the spots.
This method is expensive , uneconomical
especially when a large set of data is
required. Another drawback is that, the
interviewees could lie or have forgotten
some facts which lead to inaccurate data
being recorded.
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Telephone interview
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This entails calling interviewees via
the telephone asking them a set of
questions.
This method is suitable for radio or
television research activities.
One drawback of this method is that
only those who can be called can
give the answer.
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Mailed questionnaires
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This involves sending out questionnaires
via mail to people and expecting them to
be replied.
Generally speaking, this method is not
effective as only a relatively small
percentage of the posted ever returned.
Those returned questionnaires could be
biased in one way or another because
respondents could refer to another for
answers
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Abstracts from published statistics
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This involves abstracting part of published
statistics for one’s own use.
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In Brunei, the task of compiling national statistics
rests with the ‘Economic Planning Unit’. It is
responsible for making periodical statistical
figures for Brunei such as consumer price index,
values of total imports, exports, GDP, electricity
consumption etc.
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Normally each government department has their
own personals to deal with own statistics figures.
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Tips in designing questions for
interview
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Objective of the interview must be clearly
explained at the beginning.
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Questions must be simple and easily
understood.
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It must be clear. i.e. not ambiguous. Each
question must be capable of only one
interpretation.
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Questions should be as short as
possible. Long questions can bore
the people.
If possible, ready made answers
should be prepared i.e. ticking little
boxes.
If there are many interviewers, then
each of them should be trained in
order to get consistent answers.
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Recap
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Define Statistics
Distinguish between the four scales
Explain two main areas
Explain uses of Statistics
Show types of Statistical Data
Give some concepts used in statistics
Explain methods used in data collection
List out tips in designing interview
questions
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References
:
Lecture & Tutorial Notes from Department of Business & Management,
Institute Technology Brunei, Brunei Darussalam.
ACT Education Solutions (2005) Global Assessment Certificate – Student
Manual, ACT Education Solutions Limited, Australia
MDIS (2010) Diploma in Business Management – Course Study Booklet,
Management Development Institute of Singapore Pte Ltd, Singapore.
General Studies Department (2012), Introduction to Statistics : Lecture
Notes & Slides, Brunei Polytechnic, Brunei Darussalam
Phua, S. et al (1991). Statistics for Business (2nd Edition). FT Law & Tax
Asia Pacific : Singapore
Weiers , R.M. (2008)
Introduction to Business Statistics (6th
Edition). Thompson South-Western : Canada
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