Introduction to Mathematics for Business Studies

Lecture 1

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Assessment 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 StatisticsRonald M.Weirs

Your attendance is important. 15 % comes from tutorial participation. 15 % comes from assignment.

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Structure of your lecture

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

You will not be asked simple definitions or descriptions of concepts or ideas in your test or examination.

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?

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

Nominal Scale

Ordinal Scale

Interval Scale

Ratio Scale

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Nominal Scale 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 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

It has all the characteristics of the ordinal scale.

Unlike the ordinal scale the unit of measurement allows us to describe how much more or less one object possesses than another.

There is no absolute zero level.

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The Ratio Scale

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.

Examples include weights, distances, money, election votes .

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Two main areas of Statistics

Descriptive statistics• Consists of methods of organizing, displaying

and describing data by using tables, graphs and summary measures.

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

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 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

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

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

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

A parameter is a numerical measure used to describe an entire population.

The value is a fixed constant.

E.g. the average height of Bruneians.

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Sample statistic

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

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 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

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 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

This involves abstracting part of published statistics for one’s own use.

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.

Normally each government department has their own personals to deal with own statistics figures.

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Tips in designing questions for interview

Objective of the interview must be clearly explained at the beginning.

Questions must be simple and easily understood.

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

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