Introduction to business mathematics

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Introduction to Statistics

Idham Fahumy

Statistics, Data, &

Statistical Thinking


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Course administration

2

STA001, TT-term 2, 2012

10:30-12:30 13:00-15:00 16:30-18:30 18:30-20:30

Sun

Consultation

STA001

STA001 (L),

ACIM1,DIB1,DIB3-

adv,DIB1(E),Audi

Mon

STA001(T), ACIM1,

B1-04

STA001(T)DIB1(M)-

DIB3-adv B1-04

STA001(T), DIB1(E)

B1-04

Lecturer: Idham Fahmy

Phone: 3345 481Email: [email protected]

Faculty of Management and Computing,

MNU

STA001-Introduction to Statistics


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Objectives

At the end of this topic, students will be able to:

To present a broad overview of the subject of

statistics and its applications To distinguish between Descriptive and Inferential

statistics.

To discuss sources of data

To discuss types of data

3 STA001-Introduction to Statistics Faculty of Management and Computing,MNU


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What is statistics?

4 STA001-Introduction to Statistics Faculty of Management and Computing,MNU


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Introduction

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Definition of Statistics:

1. A collection of quantitative data pertaining

to a subject or group. Examples are sales,

income, employment statistics etc.2. The science that deals with the collection,

tabulation, analysis, interpretation, and

presentation of quantitative data

STA001-Introduction to Statistics Faculty of Management and Computing,

MNU


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WHAT IS MEANT BY STATISTICS?

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a branch of mathematics that provides techniques

to analyze whether or not your data is significant(meaningful)

Statistical applications are based on probability

statements

Nothing is proved with statistics

Statistics are reported

Statistics report the probability that similar results

would occur if you repeated the experiment For a layman, Statistics means numerical

information expressed in quantitative terms. This

information may relate to objects, subjects,

activities, phenomena, or regions of space.STA001-Introduction to Statistics Faculty of Management and Computing,MNU


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WHAT IS MEANT BY STATISTICS?

Faculty of Management and Computing, MNU

STA001-Introduction to Statistics7

Why?

1.Collecting Data

e.g. Survey

2. Presenting Data

e.g., Charts & Tables

3. Characterizing Data

e.g., Average

DataAnalysis

Decision-

Making

1984-1994 T/Maker Co.

1984-1994 T/Maker Co.


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Data are numerical facts and figures fromwhich conclusions can be drawn. Such

conclusions are important to the decision-making

processes of many professions and

organizations.

For example: government officials use conclusions drawn from

data on unemployment and inflation to make

policy decisions.

Financial planners use recent trends in stockmarket prices to make investment decisions


STA001-Introduction to Statistics


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Businesses decide which products to develop

and market by using data that reveal consumer

preferences.

Production supervisors use manufacturing data to

evaluate, control, and improve product quality.

Politicians rely on data from public opinion pollsto formulate legislation and to devise campaign

strategies.

Physicians and hospitals use data on the

effectiveness of drugs and surgical procedures toprovide patients with the best possible treatment.

STA001-Introduction to StatisticsFaculty of Management and Computing,

MNU


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Major characteristics of statistics

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Statistics are the aggregates of facts. It means asingle figure is not statistics. For example,national income of a country for a single year is

not statistics but the same for two or more years

is statistics.

Statistics are affected by a number of factors. Forexample, sale of a productdepends on a numberof factors such as its price, quality, competition,

the income of the consumers, and so on

Statistics must be reasonably accurate. Wrongfigures, if analysed, will lead toerroneousconclusions. Hence, it is necessary that

conclusions must be based on accurate figures.STA001-Introduction to Statistics Faculty of Management and Computing,

MNU


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Major characteristics of statistics

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Statistics must be collected in a systematicmanner. If data are collected in ahaphazardmanner, they will not be reliable and will lead to

misleading conclusions.

Collected in a systematic manner for a pre-determined purpose

Lastly, Statistics should be placed in relation to

each other. If one collects data unrelated to each

other, then such data will be confusing and will

not lead to any logical conclusions. Data should

be comparable over time and over space.


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Statistics deals with numbers

Need to know nature of numbers collected

Continuous variables: type of numbers associated

with measuring or weighing; any value in a

continuous interval of measurement.

Examples:

Weight of students, height of plants, time to flowering

Discrete variables: type of numbers that are

counted or categorical

Examples:

Numbers of boys, girls, insects, plants


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Can you figure out

Which type of numbers (discrete or continuous?) Numbers of persons preferring Brand X in 5

different islands

The weights of high school seniors

The lengths of banana leaves

The number of seeds germinating

Answers: all are discrete except the 2nd and 3rd

examples are continuous.


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Populations and Samples Population includes all members of a group

Example: all 12th grade students in CHSE

Sample

Used to make inferences about large populations

Samples are a selection of the population Example: Gift shops in Majeedhee Magu

Why the need for statistics?

Statistics are used to describe sample populations asestimators of the corresponding population

Many times, finding complete information about apopulation is costly and time consuming. We can usesamples to represent a population.


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Sample Populations avoiding

Bias

Individuals in a sample population Must be a fair representation of the entire pop.

Therefore sample members must be randomly

selected (to avoid bias)

Example: if you were looking at strength instudents: picking students from the football team

would NOT be random


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Is there bias? A cage has 1000 rats, you pick the first 20 you can

catch for your experiment

A public opinion poll is conducted using the telephone

directory

You are conducting a study of a new diabetes drug;

you advertise for participants in the newspaper and

TV

All are biased: Rats-you grab the slower rats.

Telephone-you call only people with a phone

(wealth?) and people who are listed (responsible?).

Newspaper/TV-you reach only people with newspaper

(wealth/educated?) and TV( wealth?).STA001-Introduction to Statistics Faculty of Management and Computing,

MNU


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SOURCES OF STATISTICAL DATA

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Researching problems involving topics suchas crime, health, imports and exports,production, hourly wages etc. generallyrequires published data. Statistics on these

and information on thousands of other topicscan be found in published articles, journals,magazines, WWW.

Published data are not always available on a

given subject. In such cases, information willhave to be collected and analyzed. One wayof collecting data is through questionnaires.


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Primary and Secondary Data

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Secondary data: They already exist in someform: published or unpublished - in anidentifiable secondary source. They are,generally, available from published source(s),

though not necessarily in the form actuallyrequired.

Primary data: Those data which do not

already exist in any form, and thus have to becollected for the first time from the primarysource(s). By their very nature, these data requirefresh and first-time collection covering the wholepopulation or a sample drawn from it.


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What information in the

NID application form canbe used to generate

some indicators.


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What information in

the application form

can be used togenerate some

indicators.


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Two phases of statistics

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Descriptive Statistics:

Describes the

characteristics of a

product or process using

information collected on it.

Inferential Statistics:

Draws conclusions on

unknown processparameters based on

information contained in a

sample.

Uses probabilitySTA001-Introduction to Statistics Faculty of Management and Computing,

MNU

Descriptive objectives/ researchquestions

Descriptive statistics

Comparative objectives/hypotheses

Inferential Statistics


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Descriptive Statistics

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Involves

Collecting Data

Presenting Data Characterizing Data

Purpose

Describe Data

X = 30.5 S2 = 113

0

25

50

Q1 Q2 Q3 Q4

$


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Descriptive Statistics

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EXAMPLE:

A poll found that 49% of the people in asurvey knew the name of the first president ofthe Maldives. The statistic49 describes thenumber out of every 100 persons who knewthe answer.


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TV networks constantly monitor the popularityof their programs by hiring research firms andother organizations to sample the preferencesof TV viewers.

The accounting department of a large firm willselect a sample of the invoices to check foraccuracy for all the invoices of the company.

Ice-cream tasters tast a few spoon of ice-cream to make a decision with respect to allthe ice-cream waiting to be released for sale.


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STA001-Introduction to Statistics25

Involves

Estimation

Hypothesis

Testing

Purpose

Make Decisions

About PopulationCharacteristics

Population?


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TYPES OF VARIABLES

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Qualitativeor Attribute variable:when thecharacteristic or variable being studied iscategorical or non-proportional.

EXAMPLES:Gender (male, female), type of

automobile owned, Island of birth, eye color,etc.

Quantitative variable:when the variable canbe reported non-categorical or proportional.

EXAMPLES:Balance in your checkingaccount, salaries of faculty members, numberof children in a family etc.


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TYPES OF VARIABLES (continued)

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Quantitative variablescan be classified aseither discreteor continuous.

Discrete Variables:can only assume certainvalues and there are usually gapsbetween

the values.

EXAMPLE:The number of bedrooms in ahouse (1, 2, 3, ..., etc.).

Continuous Variables:can assume any valuewithin a specific range.

EXAMPLE:The time it took to fly from Male toColombo (Sri Lanka).


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SUMMARY OF TYPES OF VARIABLES

Data

Qualitative orattribute Quantitativeornumerical

Discrete

Continuous

Type of car owned.Color of pens.

Number of children.Time taken for an exam.


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Statistics for Business Use

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All published statistics are part of managementinformation generated as raw data and in treated form. We may have tables of output, sales, stock

levels, etc; charts of production, machine utilization,

productivity, etc; ratios of stock turnover, gross profit, net profit,

working capital, etc.

Countless analysis will be made of products,customer trends, sales areas, sales periods,order size, distribution method, maintenanceprograms, vehicle usage, cash flow, etc.

All such information requires us to be aware of

statistical techniques, familiar with statisticalar on a reciate of its uses.STA001-Introduction to Statistics Faculty of Management and Computing,

MNU

IMPORTANCE OF STATISTICS IN


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IMPORTANCE OF STATISTICS INBUSINESS

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There are three major functions in any business

enterprise in which the statistical methods are useful. The planning of operations: This may relate to

either special projects or to the recurring activitiesof a firm over a specified period.

The setting up of standards: This may relate to thesize of employment, volume of sales, fixation ofquality norms for the manufactured product, norms for

the daily output, and so forth.

The function of control: This involves comparisonof actual production

achieved against the norm or target set earlier. In

case the production has fallen short of the target, it

gives remedial measures so that such a deficiency

does not occur again.STA001-Introduction to Statistics Faculty of Management and Computing,

MNU


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Precision and Accuracy

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Precision

The precision of a measurement is

determined by how reproducible that

measurement value is.

For example if a sample is weighed by a

student to be 42.58 g, and then measured

by another student five different times with

the resulting data: 42.09 g, 42.15 g, 42.1 g,42.16 g, 42.12 g Then the original

measurement is not very precise since it

cannot be reproduced.STA001-Introduction to Statistics Faculty of Management and Computing,

MNU


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Precision and Accuracy

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Accuracy

The accuracy of a measurement is determined by

how close a measured value is to its true value.

For example, if a sample is known to weigh 3.182g, then weighed five different times by a student

with the resulting data: 3.200 g, 3.180 g, 3.152 g,

3.168 g, 3.189 g

The most accurate measurement would be 3.180

g, because it is closest to the true weight of the

sample.

STA001-Introduction to Statistics Faculty of Management and Computing,MNU


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Application Areas

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Economics

Forecasting

Demographics

Sports

Individual & TeamPerformance

Engineering

Construction

Materials

Business

Consumer Preferences Financial Trends



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LIMITATIONS OF STATISTICS

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Statistics has a number of limitations, pertinent among

them are as follows There are certain phenomena or concepts where

statistics cannot be used. This is because thesephenomena or concepts are not amenable tomeasurement.

For example, beauty, intelligence, courage cannot bequantified. Statistics has no place in all such caseswhere quantification is not possible.

Statistics reveal the average behaviour, the normal orthe general trend. An application of the 'average'

concept if applied to an individual or a particularsituation may lead to a wrong conclusion andsometimes may be disastrous. For example, one may be misguided when told that the

average household income is Rf 5000, but there maybe

households with 10000-20000 income while fewSTA001-Introduction to Statistics Faculty of Management and Computing,MNU



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Since statistics are collected for a particular

purpose, such data may not be relevant or useful

in other situations or cases. For example, secondary data (i.e., data originally

collected by someone else) may not be useful for

the other person.

Statistics are not 100 per cent precise as isMathematics or Accountancy. Those who use

statistics should be aware of this limitation.

In statistical surveys, sampling is generally used

as it is not physically possible to cover all the

units or elements comprising the universe. The

results may not be appropriate as far as the

universe is concerned. Moreover, different

surveys based on the same size of sample butSTA001-Introduction to Statistics Faculty of Management and Computing,

MNU


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At times, association or relationship between two

or more variables is studied in statistics, but sucha relationship does not indicate cause and effect

relationship. It simply shows the similarity or

dissimilarity in the movement of the two variables.

In such cases, it is the user who has to interpretthe results carefully, pointing out the type of

relationship obtained.

A major limitation of statistics is that it does not

reveal all pertaining to a certain phenomenon.

The user of Statistics has to be well informed and

should interpret Statistics keeping in mind all

other aspects having relevance on the given

problem.STA001-Introduction to Statistics Faculty of Management and Computing,

MNU


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Misuses of Statistics

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Sources of data not given: In the absence of

the source, the reader does not know how far thedata are reliable. Further, if he/she wants to refer

to the original source, he/she is unable to do so

Defective data: This may be done knowingly inorder to defend one's position or to prove a

particular point. For example, in case of data

relating to unemployed persons, the definition

may include even those who are employed,

though partially. The question here is how far it is

justified to include partially employed persons

amongst unemployed ones.STA001-Introduction to Statistics Faculty of Management and Computing,

MNU


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Unrepresentative sample: In conducting surveys

we need to choose a sample from the givenpopulation or universe.

The sample may turn out to be unrepresentative of the

universe.

One may choose a sample just on the basis ofconvenience.

Inadequate sample: Earlier, we have seen that asample that is unrepresentative of the universe is amajor misuse of statistics. This apart, at times one

may conduct a survey based on an extremely

inadequate sample. For example, in a city we may

find that there are 100,000 households. When we

have to conduct a household survey, we may take a

sample of merely 100 households comprising only 0.1STA001-Introduction to Statistics Faculty of Management and Computing,

MNU

Mi f St ti ti


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Unfair Comparisons

An important misuse of statistics is making unfair comparisons

from the data collected. For instance, one may construct an index of production

choosing the base year where the production was much less.Then he may compare the subsequent year's production fromthis low base. Such a comparison will undoubtedly give a rosypicture of the production though in reality it is not so.

Another source of unfair comparisons could be when one makesabsolute comparisons instead of relative ones. An absolutecomparison of two figures, say, of production or export, mayshow a good increase, but in relative terms it may turnout to bevery negligible.

Another example of unfair comparison is when the population intwo cities is different, but a comparison of overall death rates anddeaths by a particular disease is attempted. Such a comparisonis wrong. Likewise, when data are not properly classified or whenchanges in the composition of population in the two years are nottaken into consideration, comparisons of such data would beunfair as they would lead to misleading conclusions.STA001-Introduction to Statistics Faculty of Management and Computing,MNU


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Unwanted conclusions:Another misuse of statistics maybe on account of unwarranted conclusions. This may be asa result of making false assumptions.

For example, while making projections of population in thenext five years, one may assume a lower rate of growth

though the past two years indicate otherwise. Sometimes one may not be sure about the changes in

business environment in the near future. In such a case,one may use an assumption that may turn out to be wrong.

Another source of unwarranted conclusion may be the use

of wrong average. Suppose in a series there are extremevalues, one is too high while the other is too low, such as800 and 50. The use of an arithmetic average in such acase may give a wrong idea. Instead, Median or harmonicmean would be proper in such a case.


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Confusion of correlation and causation In statistics, several times one has to examine the

relationship between two variables.

A close relationship between the two variables

may not establish a cause-and-effect-relationship

in the sense that one variable is the cause and

the other is the effect. It should be taken as

something that measures degree of association

rather than try to find out causal relationship..


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Statistical Computer Packages

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Typical Software SAS

SPSS

MINITAB

Excel

Need Statistical

Understanding Assumptions

Limitations



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End of Topic

Introduction to business mathematics

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