1. LESSON# 1
INTRODUCTION TO STATISTICS
STAT101/MATH 107 (Statistical Methods)
Department of Statistics
FC College University, Lahore
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2. WHAT IS STATISTICS
The mathematical science that deals
with the collection, presentation,
analysis and interpretation of data.
There are two main branches of
statistics : descriptive statistics and
inferential statistics.
6. • Descriptive statistics and inferential statistics are inter-related.
• If the purpose of the study is to examine and explore information for its own natural
interest only, the study is descriptive.
• However, if the information is obtained from a sample of a population and the purpose
of the study is to use that information to draw conclusions about the population, the
study is inferential.
• Thus, a descritpive study may be performed either on a sample or on a population.
Only when an inference is made about the population, based on information obtained
from the sample, does the study become inferential.
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7. EXAMPLE 3:
The Following Table
Displays The Voting
Results For The 1948
Presidential Election.
Ticket Votes Percentage
Truman-Barkely (Democratic) 24,179,345 49.7
Dewey-Warrab (Republican) 21,991,291 45.2
Thurmond-Wright (States
Rights)
1,176,125 2.4
Wallac-Taylor (Progressive) 1,157,326 2.4
Thomas- Smith (Socialist) 139,572 0.3
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This study is descriptive statistics. It is a summary of
the votes cast by U.S. voters in the 1948 Presidential
election. No inferences are made.
9. IDENTIFY WHETHER THE STATEMENT DESCRIBES
INFERENTIAL STATISTICS OR DESCRIPTIVE STATISTICS:
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a) The average age of the students in a statistics class is 21 years.
b) The chances of winning the California Lottery are one chance in twenty-two
million.
c) There is a relationship between smoking cigarettes and getting emphysema.
d) From past figures, it is predicted that 39% of the registered voters in California
will vote in the June primary.
descriptive
Inferential
Inferential
Inferential
10. POPULATION AND SAMPLE
THE ENTIRE GROUP OF INDIVIDUALS TO BE STUDIED IS CALLED THE POPULATION.
AN INDIVIDUAL IS A PERSON OR OBJECT THAT IS A MEMBER OF THE POPULATION
BEING STUDIED.
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11. (i)The coach wants to know which uniform the
basketball team wants to wear, but he only asks the
starting five.
(ii) A record store manager asks customers who make a
purchase how many hours of music they listen to each
day.
Population Sample
The basketball team The starting five
Population Sample
Music store customer Customers who make a
purchase
EXAMPLE 5
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12. IDENTIFY THE POPULATION AND THE SAMPLE:
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Population Sample
a. A survey of 1353 American households found
that 18% of the households own a computer.
b. A recent survey of 2625 elementary school
children found that 28% of the children could
be classified obese.
c. the average weight of every sixth person
entering the mall within 3 hour period was
146 lb.
All American
Households
1353 American
Households
All Elemntary school
children
collection of 2625
elementary school
children surveyed
all people entering the
mall within the assigned
3 hour period
every 6th person entering
the mall within the 3 hour
period
13. Parameter and Statistic
A parameter is a descriptive measure computed from an entire
population of data.
A statistic(or estimate) is a descriptive measure computed from a
sample of data.
Examples
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Parameter Statistic
Proportion of all students who attended the
last home football game.
Mean height of a sample of NBA basketball
players.
Mean SAT of entering freshmen Mean number of pepperoni slices on a 12”
pizza from a sample of a certain brand of
pepperoni pizzas.
15. PRACTICE QUESTION 1
A scientist takes a big bucket of water
from a lake and counts how many
species of bacteria, bugs, and other
creepy crawlies he finds in the
bucket.
Identify the population, the sample,
the parameter, and the estimate in
this situation.
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Population :
all the species that live in the lake
Sample:
the species that are in the bucket
the estimate is the number
of species found in the bucket.
The parameter is the
number of species in
the lake
16. Practice Question II
A school takes a poll to find
out what students want to eat
at lunch. 70 students are
randomly chosen to answer the
poll questions.
What are the population, the
sample, the parameter, and
the estimate of this study?
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The population is all the students at the school,
and the parameter is the lunch preferences of
the whole school.
The sample is the 70 students polled, and
their responses to the poll are the estimate.
17. DETERMINE WHETHER THE NUMERICAL VALUE IS A
PARAMETER OR A STATISTICS (AND EXPLAIN):
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a) A recent survey by the alumni of a major university indicated that the
average salary of 10,000 of its 300,000 graduates was 125,000.
b) The average salary of all assembly-line employees at a certain car
manufacturer is $33,000.
c) The average late fee for 360 credit card holders was found to be
$56.75.
statistic – part of 300,000 graduates are surveyed
parameter – all assembly-line employees were included in the
study
statistic – 360 credit cards were examined (not all)
18. • The collection of information from the
elements of a population or a sample is
called a survey.
• A survey that includes every number of
the population is called a census.
• The technique of collecting information
from a portion of the population is
called a survey sample
• As an example, if we collect information
on the 2009 incomes of all families in
Connecticut, it will be referred to as a
census. On the other hand, if we collect
information on the 2009 incomes of 50
families from Connecticut, it will be
called a sample survey.
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19. The experimental unit for a study refers to the object
under study.
The first step in detailing data collection protocol is to
define the experimental unit. An experimental or
sampling unit is the person or object that will be studied
by the researcher.
This is the smallest unit of analysis in the experiment
from which data will be collected.
For example, depending on the objectives, experimental
or sampling unit can be individual persons, students in a
classroom, the classroom itself, an animal or a litter of
animal, patients from a doctor’s office, houses
Experimental Unit
(Sampling Unit)
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20. EXAMPLE 6
Answer the following Questions;
a) Identify the variable and experimental unit for
this study.
Ans: Since the engineers collected data at each of
50 intersections, the experimental unit is an
intersection without a left-turn-only lane. The
variable measured is the total number of cars
turning left hat were involved in an accident.
b) Describe the target population and the sample.
Ans: The goal of the study is to develop guidelines
for the installation of left-turn lanes at all major
Lexington intersections; consequently, the target
population consists of all major intersections in the
city. The sample consists of the subset of 25
intersections monitored by the engineers.
c) What inference do the transportation engineers
want to make?
Ans: The engineers will use the sample data to
estimate the rate at which left-turn accidents occur
at all major Lexington intersections. ( We learn, in
Chapter 7, that this estimate is the number of left-
tun accidents in the sample divided by the total
number of cars making left turns in the sample. )
Engineers with the university of Kentucky
Transportation Research Program have collected data
on accidents occurring at intersections in Lexington,
Kentucky. One of the goals of the study was to
estimate the rate at which left-turn accidents occur at
intersections without left-turn-only lanes. This
estimate will be used to develop numerical warrants (
or guidelines ) for the installation of left-turn lanes at
all major Lexington intersections. The engineers
collected data at each of 50 intersections without left-
turn-only lanes over a 1-year period. At each
intersection, they monitored traffic and recorded the 20
21. A COLLECTION OF FACTS FROM
WHICH CONCLUSIONS MAY BE
DRAWN IS REFERRED AS DATA.
Data: is a collection of facts
such as numbers, words,
measurements, observations
or just description of things.
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22. Variable: A measurable quantity which can vary
from one individual or object to another is called a
variable.
Example: height, age, number of siblings, martial
status, eye color, etc.
Constant: A quantity which can assume only one
value is called a constant.
Examples of constant are ∏=3.14159, e=2.71828,
etc.
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23. Qualitative Variable
Quantitative Variable: A variable is one which can
assume a numerical value, for example, balance in
your checking account, minutes remaining in class,
number of children in a family. height of plant, weight
of grains, number of students in class etc. Quantitative
variable can further be placed into two types
depending upon the type of measurement possible.
Continuous
variables
Discrete
variables;
A qualitative variable is also
known as categorical variable
is one which is not capable of
taking numerical
measurements. For example,
gender, religious affiliation,
type of automobile owned,
state of birth, eye color, general
knowledge (poor, moderate,
good) etc.
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24. continuous
variable
a) A continuous variable is one that can take all possible values
in an interval on the number line. For example, The pressure in
a tire, the weight of a pork chop, or the height of students in a
class, atmospheric pressure, plant height, student height,
temperature.
b) A discrete variable is also known as discontinuous variable.
can only assume certain values and there are usually “gaps”
between values. EXAMPLE: the number of bedrooms in a
house, or the number of hammers sold at the local Home Depot
(1,2,3,…, etc.), number of students in a class, number of family
members in a house, number of plants in a row etc.
discrete
variable
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25. Measurement
Scales:
Nominal: unordered categories. This includes measurements of
categories such as gender, religion, sport etc.
Ordinal: Ordered categories. It has variable measurements of variable
categories such a size, behavior etc.
The four scales of
measurement are:
I. Nominal scale;
II. Ordinal scale;
III. Ratio scale;
IV. Interval scale
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26. Interval Scale
Interval Scale: like the ordinal level, with the additional property
that meaningful amounts of differences between data values can
be determined. There is no natural zero point.
EXAMPLE: Temperature on the Fahrenheit scale.
There is no zero point for IQ. We do not think of a person as having
no intelligence. Here’s the problem with interval scales: they don’t
have a “true zero.” For example, there is no such thing as “no
temperature.”
Ratio Scale: the interval level with an inherent zero starting
point. Differences and ratios are meaningful for this level of
measurement.
EXAMPLES: Monthly income of surgeons, or distance traveled
by manufacturer’s representatives per month.
Ratio Scale
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28. Ungrouped data (or raw data) are
data that are not organized, or if
arranged, could only be from
highest to lowest or lowest to
highest.
• Grouped data are data that are
organized and arranged into
different classes or categories.
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Data can be classified as grouped or ungrouped.
30. PRIMARY DATA
• These are the data that are collected for
the first time by an investigator for a
specific purpose.
• Primary data are ‘pure’ in the sense that no
statistical operations have been performed
on them and they are original.
• An example of primary data is Census of
Pakistan.
• These are the data that are sourced from someplace
that has originally collected it.
• This means that this kind of data has already been
collected by some researchers or investigators in the
past and is available either in published or unpublished
form.
• This information is impure as statistical operations
may have been performed on them already.
• An exmaple is an information available on the
government of Pakistan, the Department of Finance’s
website or in other repositories books, journals, etc.
SECONDARY DATA
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Source of Data Collection:
32. METHODS FOR COLLECTION OF
PRIMARY DATA
1. Direct Personal Investigation
2. Indirect Personal Investigation
3. Questionnaire Method
4. Investigation through Enumerators
5. Registrations
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33. 1. DIRECT PERSONAL
INVESTIGATION
• IN THIS METHODS, THE INVESTIGATOR INTERVIEWS THE PERSONS CONCERNED OR OBSERVES
FACTS PERSONALLY.
• THE INVESTIGATOR MAY GO TO LIVE WITH THE PEOPLE, MIX UP WITH THEM FREELY AND
GATHER THE FACTS.
• THE INFORMATION COLLECTED IN THIS WAY IS QUITE ACCURATE.
• THIS METHOD IS SLOW AND EXPENSIVE
• IT IS SUITABLE ONLY IN LABORATORY EXPERIMENTS OR LOCALIZED INQUIRES
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34. 2. INDIRECT PERSONAL
INVESTIGATION
• SOMETIMES, IT IS KNOWN THAT THE RESPONDENTS WOULD NOT
DISCLOSE THE INFORMATION AT ALL OR WOULD INTENTIONALLY
PROVIDE FALSE INFORMATION.
• FOR EXAMPLE, GOVERNMENT SERVANTS DO NOT DISCLOSE THEIR
INCOME FROM PART-TIME WORK AND THE BUSINESSMAN SELDOM
DISCLOSE THEIR TRUE INCOMES TO THE INCOME TAX AUTHORITIES.
• THIS METHOD IS USED WHEN INFORMATION TO BE COLLECTED IS
COMPLEX OR THE RESPONDENTS ARE RELUCTANT TO DISCLOSE THE
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35. 3. QUESTIONNAIRE METHOD
• THIS METHOD IS USED TO COLLECT INFORMATION FROM LITERATE PEOPLE.
• QUESTIONNAIRE IS AS AN INSTRUMENT FOR RESEARCH, WHICH CONSISTS OF A LIST OF QUESTIONS, ALONG WITH THE CHOICE OF
ANSWERS, PRINTED OR TYPED IN A SEQUENCE ON A FORM USED FOR ACQUIRING SPECIFIC INFORMATION FROM THE RESPONDENTS.
• IN GENERAL, QUESTIONNAIRES ARE DELIVERED TO THE PERSONS CONCERNED EITHER BY POST OR MAIL, REQUESTING THEM TO ANSWER
THE QUESTIONS AND RETURN IT.
• INFORMANTS ARE EXPECTED TO READ AND UNDERSTAND THE QUESTIONS AND REPLY IN THE SPACE PROVIDED IN THE QUESTIONNAIRE
ITSELF.
• THE QUESTIONNAIRE IS PREPARED IN SUCH A WAY THAT IT TRANSLATES THE REQUIRED INFORMATION INTO A SERIES OF QUESTIONS,
THAT INFORMANTS CAN AND WILL ANSWER.
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36. 4. INVESTIGATION THROUGH ENUMERATORS
• THIS METHOD IS AN ALTERNATIVE WAY TO GET INFORMATION OF PRIMARY DATA FROM RURAL
AREA.
• A NUMBER OF ENUMERATORS ARE SELECTED AND TRAINED. THEY ARE PROVIDED WITH
STANDARDIZED QUESTIONNAIRE.
• THESE ENUMERATORS GOES TO THE RESPONDENTS ALONG WITH THE QUESTIONNAIRE AND
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37. 5. REGISTRATION
• IN THIS METHOD INFORMATION IS REPORTED TO THE
APPROPRIATE AUTHORITY WHEN OR SHORTLY AFTER AN
EVENT OCCURS.
• FOR EXAMPLE, THE BIRTHS AND DEATHS ARE REGISTERED
WITH THE MUNICIPAL COMMITTEE OR CO-OPERATION IN 37
38. METHODS OF COLLECTION OF SECONDARY DATA
1. OFFICIAL SOURCES, E.G. PUBLICATIONS OF FEDERAL BUREAU OF STATISTICS, MINISTRIES OF AGRICULTURE, FINANCE, COMMUNICATIONS AND
RAILWAYS, PROVINCIAL BUREAUS OF STATISTICS AND PROVINCIAL DEPARTMENTS OF AGRICULTURE, HEALTH AND EDUCATION
2. SEMI- OFFICIAL SOURCES, E.G. PUBLICATIONS OF STATE BANK OF PAKISTAN, CENTRAL COTTON COMMITTEE, ECONOMIC RESEARCH INSTITUTES,
DISTRICT COUNCIL, MUNICIPAL COMMITTEE, WAPDA, ETC.
3. PRIVATE SOURCES, E.G. PUBLICATIONS OF TRADE ASSOCIATIONS, CHAMBERS OF COMMERCE AND INDUSTRY, MARKET COMMITTEES, ETC.
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