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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: idham.fahumy@mnu.edu.mv
Faculty of Management and Computing,
MNU
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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
5
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
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MNU
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WHAT IS MEANT BY STATISTICS?
6
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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8
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
Faculty of Management and Computing, MNU
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9
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
10
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
11
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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MNU
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12
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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MNU
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13
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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MNU
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14
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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MNU
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15
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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MNU
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16
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
17
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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MNU
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Primary and Secondary Data
18
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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MNU
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19
What information in the
NID application form canbe used to generate
some indicators.
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MNU
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20
What information in
the application form
can be used togenerate some
indicators.
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MNU
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Two phases of statistics
21
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
22
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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MNU
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Descriptive Statistics
23
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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MNU
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Inferential Statistics
24
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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MNU
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Inferential Statistics
Faculty of Management and Computing, MNU
STA001-Introduction to Statistics25
Involves
Estimation
Hypothesis
Testing
Purpose
Make Decisions
About PopulationCharacteristics
Population?
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TYPES OF VARIABLES
26
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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MNU
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TYPES OF VARIABLES (continued)
27
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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MNU
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28
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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MNU
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Statistics for Business Use
30
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
31
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
32
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
33
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.
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Application Areas
34
Economics
Forecasting
Demographics
Sports
Individual & TeamPerformance
Engineering
Construction
Materials
Business
Consumer Preferences Financial Trends
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LIMITATIONS OF STATISTICS
35
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
LIMITATIONS OF STATISTICS
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LIMITATIONS OF STATISTICS
36
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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LIMITATIONS OF STATISTICS
37
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
38
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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Misuses of Statistics
39
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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Misuses of Statistics
40
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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Misuses of Statistics
41
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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MNU
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Misuses of Statistics
42
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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MNU
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Statistical Computer Packages
43
Typical Software SAS
SPSS
MINITAB
Excel
Need Statistical
Understanding Assumptions
Limitations
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End of Topic
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