Math 1127Introductory Statistics

Dr. Carlos Almada

Office: 212 University Hall

Office Hours: Wed 7-11 am

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

Stats … Before

Stats … After

Class Web Page:

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http://facstaff.columbusstate.edu/almada_carlos/

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Math 1127: Introductory Statistics

Overview Of Statistics

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? 

Typical Problem

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

Public Elementary SchoolsGentian Georgetown Hannan Elementary Johnson Key Martin Luther King, Jr. Mathews Midland AcademyMuscogee North Columbus ElementaryReese Road Rigdon Road River Road South Columbus St. Marys Video and

Communication TechnologyWaddell Wesley Heights Wynnton

Middle Arnold Baker Blackmon Road Double Churches East Columbus Magnet

AcademyEddy Fort Marshall Midland Richards Rothschild

High Anne Elizabeth Sheperd HomeCarver Columbus Early College Academy of ColumbusHardaway Jordan Vocational Kendrick Northside Shaw Spencer

Public Middle/High Schools

Number of Students in 2008: 33,502Economically Disadvantaged: 61.00% Students with Disabilities: 12.00% English Language Learners: 2.00%

Did this District make Adequate Yearly Progress in 2008?

No

District Facts for 2008

Chapter 1 Introduction to Statistics

Overview Variables and Types of Data

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.

“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

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.

Introduction to Statistics

Definition of Population and Sample

Introduction to Statistics

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

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)

Parameters and Statistics

Parameter Population

Statistic Sample

A parameter is a numerical description of a population characteristic.

A statistic is a numerical description of a sample characteristic.

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.

Parameters and Statistics

Branches of Statistics

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

Statistics

Descriptive statistics

Inferential statistics

Involves organizing, summarizing, and displaying data.

Involves using a sample to draw conclusions about a population.

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.

Descriptive and Inferential 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

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.

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.

The Process of Statistics

Data Collection

Simple Random Sampling

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.

Simple Random Sampling (SRS)

In chapter 6 we will be interested in all possible samples of a fixed size that can be selected from a given population

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

Simple Random Sampling (SRS)

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.

Variables and Data

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…..

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.

Two Types 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.

Examples of Variables

More Examples of Variables

Age, Height, Weight Grade in Math 1127 (A=4, B=3, etc.) Temperature (K, F, C) Male (0), Female (1), Androgynous (2) Test score (e.g., SAT)

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.

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.

Types of Quantitative Variables

Variables

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 ……

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.

Data

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

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

Example of Variables and Data