Sqqs1013 ch1-a122

SQQS1013 Elementary Statistics
INTRODUCTION TOINTRODUCTION TO
StatisticsStatistics
1.1 WHAT IS STATISTICS?
• The word statistics derives from classical Latin roots,
status which means state.
• Statistics has become the universal language of the sciences.
• As potential users of statistics, we need to master both the “science” and the
“art” of using statistical methodology correctly.
• These method include:
 Carefully defining the situation
 Gathering data
 Accurately summarizing the data
 Deriving and communicating meaningful conclusions
• Nowadays statistics is used in almost all fields of human effort such as:
Education Agricultural Businesses Health
Chapter 1: Introduction to Statistics 1
Specific definition:
Statistics is a collection of procedures and principles for
gathering data and analyzing information to help people
make decisions when faced with uncertainty.

1. Sport
• Sports
A statistician may keeps records of the number of hits a baseball player gets in
a season.
• Financial
Financial advisor uses some statistic information to make reliable predictions
in investment.
• Public Health
An administrator would be concerned with the number of residents who
contract a new strain of flu virus during a certain year.
• Others
Any Idea?…..
1.2 TWO ASPECTS IN STATISTICS
Statistics has Two Aspects:
1. Theoretical / Mathematical Statistics
° Deals with the development, derivation and proof of statistical theorems,
formulas, rules and laws.
2. Applied Statistics
o Involves the applications of those theorems, formulas, rules and laws to
solve real world problems.
o Applied Statistics can be divided into two main areas, depending on how data
are used. The two main areas are:
Example applications of Statistics

Descriptive
Statistics
Consist of methods that use
results obtained from sample to
make decisions or conclusions
about a population
Applied
Statistics
Consist of method for
collecting, organizing,
displaying and
summarizing data
Inferential
Statistics
Deals with the development,
derivation and proof of statistical
theorems, formulas, rules and
laws.
Involves the applications of those
theorems, formulas, rules and laws
to solve real world problems.
Theoretical/Mathematical
Statistics
ASPECTS OF STATISTICS
Determine which of the following statements is descriptive in nature and which
is inferential.
a. Of all U.S kindergarten teachers, 32% say that “knowing the alphabet” is an
essential skill.
Chapter 1: Introduction to Statistics
Descriptive statistics Inferential statistics
• What most people think of
when they hear the word
statistics
• Includes the collection,
presentation, and description
of sample data.
• Using graphs, charts and
tables to show data.
•
• Refers to the technique of
interpreting the values resulting
from the descriptive techniques
and making decisions and
drawing conclusions about the
population
3
Example 1

b. Of the 800 U.S kindergarten teachers polled, 32% say that “knowing the
alphabet” is an essential skill.
• Why do we have to study statistics?
 To read and understand various statistical studies in related field.
 To communicate and explain the results of study in related field
using our own words.
 To become better consumers and citizens.
1.3 BASIC TERMS OF STATISTICS
• Population vs. Sample
Population Sample
• A collection of all individuals
about which information is desired.
‘Individuals’ are usually people but
could also be schools, cities, pet dogs,
agriculture fields, etc.
• There are two kinds of population:
 Finite population
When the membership of a
population can be (or could be)
physically listed.
e.g. the books in library.
 Infinite population
• A subset of the population.
Parameter
Population
Sample
Statistic
Inference

When the membership is unlimited.
e.g. the population of all people
who might use aspirin.
• Parameter vs. Statistic
Parameter Statistic
• A numerical value summarizing all
the data of an entire population.
• Often a Greek letter is used to
symbolize the name of parameter.
Average/Mean - µ
Standard deviation - σ
e.g. The “average” age at time of
admission for all students who
have ever attended our college.
• A numerical value summarizing the
sample data.
• English alphabet is used to
symbolize the name of statistic
Average/Mean - s
Standard deviation -
e.g. The “average” height, found by
using the set of 25 heights.
• Variable
A characteristic of interest about each individual element of a population
or sample.
e.g. : A student’s age at entrance into college, the color of student’s hair.
• Data value
The value of variable associated with one element of a population or
sample. This value may be a number, a word, or a symbol.
e.g. : Farah entered college at age “23”, her hair is “brown”.
• Data
The set of values collected from the variable from each of the elements
that belong to sample.
e.g. : The set of 25 heights collected from 25 students.
• Census : a survey includes every element in the population.
• Sample survey : a survey includes every element in selected sample
only.
A statistics student is interested in finding out something about the average
ringgit value of cars owned by the faculty members of our university. Each of the
seven terms just describe can be identified in this situation.
Example 2

i) Population : the collection of all cars owned by all faculty members at our
university.
ii) Sample : any subset of that population. For example, the cars owned by
members the statistics department.
iii) Variable : the “ringgit value” of each individual car.(RM)
iv) Data value : one data value is the ringgit value of a particular car. Ali’s
car, for example, is value at RM 45 000.
v) Data : the set of values that correspond to the sample obtained
(45,000; 55,000; 34, 0000 ;…).
vi) Parameter : which we are seeking information is the “average” value of all
cars in the population.
vii) Statistic : will be found is the “average” value of the cars in the sample.
1.3.1 Types of Variables
• Quantitative (numerical) Variables
 A variable that quantifies an element of a population.
e.g. the “total cost” of textbooks purchased by each student for this
semester’s classes.
 Arithmetic operations such as addition and averaging are
meaningful for data that result from a quantitative variable.
 Can be subdivided into two classifications: discrete variables and
continuous variables.
Discrete Variables Continuous Variables

 A quantitative variable that can
assume a countable number of
values.
 Can assume any values
corresponding to isolated points
along a line interval. That is, there
is a gap between any two values.
e.g. Number of courses for which
you are currently registered.
 A quantitative variable that can
assume an uncountable number
of values.
 Can assume any value along a
line interval, including every
possible value between any two
values.
e.g. Weight of books and supplies
you are carrying as you attend class
today.
• Qualitative (attribute, categorical) variables
 A variable that describes or categorizes an element of a population.
e.g.: A sample of four hair-salon customers was surveyed for their
“hair color”, “hometown” and “level of satisfaction”.
EXERCISE 1
1. Of the adult U.S. population, 36% has an allergy. A sample of 1200 randomly
selected adults resulted in 33.2% reporting an allergy.
a. Describe the population.
b. What is sample?
c. Describe the variable.
d. Identify the statistics and give its value.
e. Identify the parameter and give its value.
2. The faculty members at Universiti Utara Malaysia were surveyed on the question
“How satisfied were you with this semester schedule?” Their responses were to be
categorized as “very satisfied,” “somewhat satisfied,” “neither satisfied nor
dissatisfied,” “somewhat dissatisfied,” or “very dissatisfied.”
a. Name the variable interest.
b. Identify the type of variable.
3. A study was conducted by Aventis Pharmaceuticals Inc. to measure the adverse
side effects of Allegra, a drug used for treatment of seasonal allergies. A sample of
679 allergy sufferers in the United States was given 60 mg of the drug twice a day.
The patients were to report whether they experienced relief from their allergies as
well as any adverse side effects (viral infection, nausea, drowsiness, etc)
a. What is the population being studied?
b. What is the sample?

c. What are the characteristics of interest about each element in the
population?
d. Are the data being collected qualitative or quantitative?
4. Identify each of the following as an example of (1) attribute (qualitative) or (2)
numerical (quantitative) variables.
a. The breaking strength of a given type of string
b. The hair color of children auditioning for the musical Annie.
c. The number of stop signs in town of less than 500 people.
d. Whether or not a faucet is defective.
e. The number of questions answered correctly on a standardized test.
f. The length of time required to answer a telephone call at a certain real
estate office.
1.3.2 Types of Data
• Data is the set of values collected from the variable from each of the
elements that belong to sample.
• e.g. the set of 25 heights collected from 25 students.
• Data can be collected from a survey or an experiment.
Types of Data
Primary data
Necessary data obtained through survey
conducted by researcher
Primary Data Collection Techniques
Data is collected by researcher and obtained from
respondent
1. Face to face interview
Two ways communication where researcher(s)
asks question directly to respondent(s).
Advantages:
Precise answer.
Appropriate for research that requires huge data
collection.
Increase the number of answered questions.
Disadvantages:
Expensive.
Interviewer might influence respondent’s
responses.
Respondent refuse to answer sensitive or personal
question.
2. Telephone interview
Advantages:
Quick.
Less costly.
Wider respondent coverage.
Disadvantages:
Limited interview duration.
Demonstration cannot be performing.
Telephone is not answered.
3. Postal questionnaire
A set of questions to obtain related information of
conducted study.
Questionnaires are posted to every respondent.
Advantages:
Wider respondent coverage.
Respondent have enough time to answer
questions.
Interviewer influences can be avoided.
Lower cost.
Disadvantages:
One way interaction.
Low response rate.
Secondary data
Data obtained from published material
by governmental, industrial or
individual sources
Published records from governmental,
industrial or individual sources.
Historical data.
Various resources.
Experiment is not required.
Advantages:
Lower cost.
Save time and energy.
Disadvantages:
Obsolete information.
Data accuracy is not confirmed.

Any Idea?.......
Another technique to collect primary data
is observation. List the advantages and
disadvantages of this technique.
1.3.2.1 Scale of Measurements
• Data also can be classified by how they are categorized, counted or
measured.
• This type of classification uses measurement scales with 4 common
types of scales: nominal, ordinal, interval and ratio.
Nominal Level of Measurement Ordinal Level of Measurement
 A qualitative variable that
characterizes (or describes/names)
an element of a population.
 Arithmetic operations not meaningful
for data.
 Order cannot be assigned to the
categories.
 Example:
- Survey responses:- yes, no,
undecided,
- Gender:- male, female
 A qualitative variable that
incorporates and ordered position, or
ranking.
 Differences between data values
either cannot be determined or are
meaningless.
 Example:
- Level of satisfaction:- “very
satisfied”, “satisfied”, “somewhat
satisfied”, etc.
- Course grades:- A, B, C, D, or F

Interval Level of Measurement Ratio Level of Measurement
 Involve a quantitative variable.
 A scale where distances between
data are meaningful.
 Differences make sense, but ratios
do not (e.g., 30°-20°=20°-10°, but
20°/10° is not twice as hot!).
 No natural zero
 Example:
- Temperature scales are interval
data with 25o
C warmer than
20o
C and a 5o
C difference has
some physical meaning. Note
that 0o
C is arbitrary, so that it
does not make sense to say that
20o
C is twice as hot as 10o
C.
- The year 0 is arbitrary and it is
not sensible to say that the year
2000 is twice as old as the year
1000.
 A scale in which both intervals
between values and ratios of values
are meaningful.
 A real zero point.
 Example:
- Temperature measured in degrees
Kelvin is a ratio scale because we
know a meaningful zero point
(absolute zero).
- Physical measurements of height,
weight, length are typically ratio
variables. It is now meaningful to
say that 10m is twice as long as
5m. This is because there is a
natural zero.
Levels of Measurement
• Nominal - categories only
• Ordinal - categories with some order
• Interval - differences but no natural starting point
• Ratio - differences and a natural starting point
EXERCISE 2
1) Classify each as nominal-level, ordinal-level, interval-level or ratio-level.
Chapter 1: Introduction to Statistics
a. Ratings of newscasts in Malaysia.
(poor, fair, good, excellent)
b. Temperature of automatic popcorn poppers.
c. Marital status of respondents to a survey on
saving accounts.
d. Age of students enrolled in a marital arts course.
e. Salaries of cashiers of C-Mart stores.
10

2) Data obtained from a nominal scale
a. must be alphabetic.
b. can be either numeric or nonnumeric.
c. must be numeric.
d. must rank order the data.
3) The set of measurements collected for a particular element is (are) called
a. variables.
b. observations.
c. samples.
d. none of the above answers is correct.
4) The scale of measurement that is simply a label for the purpose of
identifying the attribute of an element is the
a. ratio scale.
b. nominal scale.
c. ordinal scale.
d. interval scale.
5) Some hotels ask their guests to rate the hotel’s services as excellent,
very good, good, and poor. This is an example of the
a. ordinal scale.
b. ratio scale.
c. nominal scale.
d. interval scale.
6) The ratio scale of measurement has the properties of
a. only the ordinal scale.
b. only the nominal scale.
c. the rank scale.
d. the interval scale.
7) Arithmetic operations are inappropriate for
a. the ratio scale.
b. the interval scale.
c. both the ratio and interval scales.
d. the nominal scale.
8) A characteristic of interest for the elements is called a(n)
a. sample.
b. data set.
c. variable.
9) In a questionnaire, respondents are asked to mark their gender as male
or female. Gender is an example of a
a. qualitative variable.
b. quantitative variable.

c. qualitative or quantitative variable, depending on how the
respondents answered the question.
10) The summaries of data, which may be tabular, graphical, or numerical,
are referred to as
a.inferential statistics.
b.descriptive statistics.
c. statistical inference.
d.report generation.
11) Statistical inference
a.refers to the process of drawing inferences about the sample based
on the characteristics of the population.
b. is the same as descriptive statistics.
c. is the process of drawing inferences about the population based on
the information taken from the sample.
d. is the same as a census.
EXERCISE 3
1. In each of this statements, tell whether descriptive or inferential statistics
have been used.
a) The average life expectancy in New Zealand is 78.49 years.
b) A diet high in fruits and vegetables will lower blood pressure.
c) The total amount of estimated losses from Tsunami flood was RM4.2
billion.
d) Researchers stated that the shape of a person’s ears is related to the
person’s aggression
e) In 2013, the number of high school graduates will be 3.2 million
students.
2. Classify each variable as discrete or continuous.
a) Ages of people working in a large factory
b) Number of cups of coffee served at a restaurant

c) The amount of a drug injected into a rat.
d) The time it takes a student to walk to school
e) The number of liters of milk sold each day at a grocery store
3. Classify each as nominal-level, ordinal level, interval-level, or ratio level.
a) Rating of movies as U, SX and LP.
b) Number of candy bars sold on a fund drive
c) Classification of automobile as subcompact, compact, standard and
luxury.
d) Temperatures of hair dryers.
e) Weights of suitcases on a commercial airline.
4. At Sintok Community College 150 students are randomly selected and asked
the distance of their house to campus. From this group a mean of 5.2 km is
computed.
a. What is the parameter?
b. What is the statistics?
c. What is the population?
d. What is the sample?
Matrix No: _______________________ Group:______
TUTORIAL CHAPTER 1
In the following multiple-choice questions, please circle the correct answer.
1. You asked five of your classmates about their height. On the basis of this
information, you stated that the average height of all students in your university
or college is 65 inches. This is an example of:
a. descriptive statistics
b. statistical inference
c. parameter
d. population
25

2. A company has developed a new computer sound card, but the average lifetime
is unknown. In order to estimate this average, 200 sound cards are randomly
selected from a large production line and tested and the average lifetime is
found to be 5 years. The 200 sound cards represent the:
a. parameter
b. statistic
c. sample
d. population
3. A summary measure that is computed from a sample to describe a characteristic
of the population is called a
a. parameter
b. statistic
c. population
d. sample
4. A summary measure that is computed from a population is called a
a. parameter
b. statistic
c. population
d. sample
5. When data are collected in a statistical study for only a portion or subset of all
elements of interest, we are using a:
a. sample
b. parameter
c. population
d. statistic
6. Which of the following is not the goal of descriptive statistics?
a. Summarizing data
b. Displaying aspects of the collected data
c. Reporting numerical findings
d. Estimating characteristics of the population
7. Which of the following statements is not true?
a. One form of descriptive statistics uses graphical techniques
b. One form of descriptive statistics uses numerical techniques
c. In the language of statistics, population refers to a group of people
d. Statistical inference is used to draw conclusions or inferences about
characteristics of populations based on sample data
8. Descriptive statistics deals with methods of:
a. organizing data
b. summarizing data
c. presenting data in a convenient and informative way
d. All of the above
9. A politician who is running for the office of governor of a state with 4 million
registered voters commissions a survey. In the survey, 54% of the 5,000

registered voters interviewed say they plan to vote for her. The population of
interest is the:
a. 4 million registered voters in the state
b. 5,000 registered voters interviewed
c. 2,700 voters interviewed who plan to vote for her.
d. 2,300 voters interviewed who plan not to vote for her
10. A company has developed a new battery, but the average lifetime is unknown.
In order to estimate this average, a sample of 500 batteries is tested and the
average lifetime of this sample is found to be 225 hours. The 225 hours is the
value of a:
a. parameter
b. statistic
c. sample
d. population
11. The process of using sample statistics to draw conclusions about true population
parameters is called
a. inferential statistics
b. the scientific method
c. sampling method
d. descriptive statistics
12. Which of the following is most likely a population as opposed to a sample?
a. Respondents to a magazine survey
b. The first 10 students completing a final exam
c. Every fifth student to arrive at the book store on your campus
d. Registered voters in the State of Michigan
13. Researchers suspect that the average number of credits earned per semester by
college students is rising. A researcher at Michigan State University (MSU)
wished to estimate the number of credits earned by students during the fall
semester of 2003 at MSU. To do so, he randomly selects 500 student
transcripts and records the number of credits each student earned in the fall term
2003. He found that the average number of semester credits completed was
14.85 credits per student. The population of interest to the researcher is
a. all MSU students
b. all college students in Michigan
c. all MSU students enrolled in the fall semester of 2003
d. all college students in Michigan enrolled in the fall semester of 2003
14. The collection and summarization of the graduate degrees and research areas of
interest of the faculty in the University of Michigan of a particular academic
institution is an example of
b. descriptive statistics
c. a parameter
d. a statistic

15. Those methods involving the collection, presentation, and characterization of a
set of data in order to properly describe the various features of that set of data
are called
b. the scientific method
c. sampling method
d. descriptive statistics
16. The estimation of the population average student expenditure on education
based on the sample average expenditure of 1,000 students is an example of
b. descriptive statistics
c. a parameter
a. a statistic
17. A study is under way in a national forest to determine the adult height of pine
trees. Specifically, the study is attempting to determine what factors aid a tree
in reaching heights greater than 50 feet tall. It is estimated that the forest
contains 32,000 pine trees. The study involves collecting heights from 500
randomly selected adult pine trees and analyzing the results. The sample in the
study is
a. the 500 randomly selected adult pine trees
b. the 32,000 adult pine trees in the forest
c. all the adult pine trees taller than 50 feet
d. all pine trees, of any age in the forest
18. The classification of student major (accounting, economics, management,
marketing, other) is an example of
a. a categorical random variable.
b. a discrete random variable
c. a continuous random variable
d. a parameter.
19. Most colleges admit students based on their achievements in a number of
different areas. The grade obtained in senior level English course (A, B, C, D,
or F) is an example of a ________________, or ________________ variable.
20. For each of the following examples, identify the data type as nominal, ordinal,
or interval.
a. The letter grades received by students in a computer science class
________________
b. The number of students in a statistics course

________________
c. The starting salaries of newly Ph.D. graduates from a statistics program
________________
d. The size of fries (small, medium, large) ordered by a sample of Burger King
customers. _____________________
e. The college you are enrolled in (Arts and science, Business, Education, etc.)
_________________

Sqqs1013 ch1-a122

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