Math 1127 Introductory Statistics

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Math 1127Introductory Statistics

• Dr. Carlos Almada
• Office 212 University Hall
• Office Hours Wed 7-11 am

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Math 1127 Class Format

• My share
• Lectures, Blackboard, Powerpoint, Slides
• Problem Solving
• Discussion
• Office Hours

• Your share
• Be prepared!
• Arrive on time
• Stay until end of session
• Do the homework
• Provide feedback

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Stats Before
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Stats After
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Class Web Page

• Go to
• http//facstaff.columbusstate.edu/almada_carlos/
• Click on
• Math 1127 Introductory Statistics

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Overview Of Statistics
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Typical Problem

• Recent news programs have found that dairies
  companies have been under filling milk containers
  sent to public school lunch programs. This under
  filling of containers costs school districts,
  that is, taxpayers, mega-bucks.

How could you discover if containers in your
school district were being under filled? 
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Public Elementary Schools

• Allen
• Benning Hills
• Blanchard
• Brewer
• Britt David Elementary Computer Magnet Academy
• Clubview
• Cusseta Road
• Davis
• Dawson
• Dimon Elementary
• Double Churches
• Downtown Elementary Magnet Academy
• Eastway
• Edgewood
• Forrest Road
• Fox

Gentian Georgetown Hannan Elementary Johnson
Key Martin Luther King, Jr. Mathews Midland
Academy Muscogee North Columbus Elementary Reese
Road Rigdon Road River Road South Columbus
St. Marys Video and Communication
Technology Waddell Wesley Heights Wynnton
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Public Middle/High Schools
Middle Arnold Baker Blackmon Road Double
Churches East Columbus Magnet Academy Eddy Fort
Marshall Midland Richards Rothschild
High Anne Elizabeth Sheperd Home Carver
Columbus Early College Academy of
Columbus Hardaway Jordan Vocational Kendrick
Northside Shaw Spencer
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District Facts for 2008
Number of Students in 2008
33,502 Economically Disadvantaged 61.00
Students with Disabilities 12.00 English
Language Learners 2.00 Did this District
make Adequate Yearly Progress in 2008?
No
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Chapter 1 Introduction to Statistics

• Overview
• Variables and Types of Data

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Introduction to Statistics

• Definition Statistics is the science of

C
Collecting
O
Organizing
D
Displaying
I
Interpreting
A
Analyzing
Data
in order to make decisions.
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Introduction to Statistics

• Data is the plural of Datum (Latin for
  given).
• Consists of information coming from counts,
  observations, measurements, or responses on a
  set of objects.
• The objects can be anything, e.g., people,
  animals

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Introduction to Statistics

• Definition of Population and Sample
• Population the complete collection of all
  individuals or objects (scores, people,
  measurements, and so on) to be studied.
• Sample a subcollection of members selected from
  a population and from which the desired
  information is collected.

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Introduction to Statistics

• Definition of Population and Sample

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Therefore, There Is

• Population Data or Census
• Consists of data collected from every member of
  a population
• Sample Data
• Consists of data collected from the members of a
  sample of a population

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Population and Sample

• Example In a recent survey, 250 college students
  at Union College were asked if they smoked
  cigarettes regularly. 35 of the students said
  yes. Identify the population and the sample.

Responses of all students at Union College
(population)
Responses of students in survey (sample)
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Parameters and Statistics

• A parameter is a numerical description of a
  population characteristic.

• A statistic is a numerical description of a
  sample characteristic.

Parameter
Population
Statistic
Sample
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Parameters and Statistics

• Example Decide whether the numerical value
  describes a population parameter or a sample
  statistic.

• A recent survey of a sample of 450 college
  students reported that the average weekly income
  for students is 325.

Because the average of 325 is based on a sample,
this is a sample statistic.

• The average weekly income for all students is
  405.

Because the average of 405 is based on a
population, this is a population parameter.
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Branches of Statistics

• The study of statistics has two major branches
  descriptive statistics and inferential statistics.

Statistics
Inferential statistics
Descriptive statistics
Involves organizing, summarizing, and displaying
data.
Involves using a sample to draw conclusions about
a population.
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Descriptive and Inferential Statistics

• Example In a recent study, volunteers who had
  less than 6 hours of sleep were four times more
  likely to answer incorrectly on a science test
  than were participants who had at least 8 hours
  of sleep.
• Decide which part is the descriptive statistic
  and what conclusion might be drawn using
  inferential statistics.

The statement four times more likely to answer
incorrectly is a descriptive statistic. An
inference drawn from the sample is that all
individuals sleeping less than 6 hours are more
likely to answer science questions incorrectly
than individuals who sleep at least 8 hours.
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Descriptive and Inferential Statistics
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The Process of Statistics

• Step 1 Identify a Research Objective
• Researcher must determine question he/she wants
  answered.
• Identify the group to be studied. This group is
  called the population.
• An individual is a person or object that is a
  member of the population being studied

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The Process of Statistics

• Step 2 Collect the information needed to
  answer the questions.
• In conducting research, we typically look at a
  subset of the population, called a sample.
• Step 3 Organize and summarize the
  information.
• Descriptive statistics consists of organizing
  and summarizing the information collected.
  Consists of charts, tables, and numerical
  summaries.

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The Process of Statistics

• Step 4 Draw conclusions from the
  information.
• The information collected from the sample is
  generalized to the population.
• Inferential statistics uses methods that
  generalize results obtained from a sample to the
  population and measure their reliability.

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• Data Collection
• Simple Random Sampling

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Simple Random Sampling (SRS)
We say that a sample of size n from a population
of size N is obtained through simple random
sampling if every possible sample of size n has
an equally likely chance of occurring. The
sample is then called a simple random sample.
In chapter 6 we will be interested in all
possible samples of a fixed size that can be
selected from a given population
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Simple Random Sampling (SRS)
Suppose a study group of consists of 5 students
Bob, Patricia, Mike, Jan, and Maria. Two of the
students must go to the board to demonstrate a
homework problem. List all possible samples of
size 2 (without replacement).

• Bob, Patricia
• Bob, Mike
• Bob, Jan
• Bob, Maria
• Patricia, Mike

• Patricia, Jan
• Patricia, Maria
• Mike, Jan
• Mike, Maria
• Jan, Maria

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Steps for Obtaining a SRS

• Obtain a frame that lists all the individuals in
  the population of interest.
• Number the individuals in the frame 1 - N.
• Use a graphing calculator, or statistical
  software to randomly generate n numbers where n
  is the desired sample size.

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Variables and Data
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Variables

• Variables are the characteristics of the
  individuals within the population.
• Mathematically speaking, a variable is a function
  that assigns to each member of a population an
  output that can be numerically or non-numerically
  valued.
• According to this output we have..

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Two Types of Variables
A Qualitative or Categorical variable allows for
the classification of individuals based on some
attribute or characteristic. It is a
non-numerically valued variable.
A Quantitative variable provides numerical
measures of individuals. Arithmetic operations
such as addition and subtraction can be performed
on the values of the quantitative variable and
provide meaningful results.
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Examples of Variables
Determine whether the following variables are
qualitative or quantitative.
a) Type of wood used to build a kitchen table. b)
Number of yards Tiger Woods hits his drives. c)
Number of times your Internet service goes down
in the next 30 days.
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More Examples of Variables

• Age, Height, Weight
• Grade in Math 1127 (A4, B3, etc.)
• Temperature (K, F, C)
• Male (0), Female (1), Androgynous (2)
• Test score (e.g., SAT)

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Types of Quantitative Variables
A discrete variable is a quantitative variable
that either has a finite number of possible
values or a countable number of possible values.
A continuous variable is a quantitative variable
that has infinitely many possible values that
correspond to some continuous scale that covers a
range of values without gaps, interruptions, or
jumps. A continuous variable can be measured to
any desired level of accuracy.
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Types of Quantitative Variables
Determine whether the following quantitative
variables are continuous or discrete.
a) Number of yards Tiger Woods hits his
drives. b) Number of times your Internet service
goes down in the next 30 days.
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Variables
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Data

• The list of observations a variable assumes is
  called data.
• While gender is a variable, the observations,
  male or female, are data.
• According to the type of data the variables
  represents, we can have

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Data

• Qualitative data are observations corresponding
  to a qualitative variable.
• Quantitative data are observations corresponding
  to a quantitative variable.
• Discrete data are observations corresponding to a
  discrete variable.
• Continuous data are observations corresponding to
  a continuous variable.

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Example of Variables and Data
Here is part of the data set (a spreadsheet) in
which Cyber Stat Corporation records information
about its employees

• Each row records data on one individual.
• Each column contains the values of one variable
  for all the individuals.