Math 1231

1
Introduction

• Math 1231

2
Why do I have to take this class?

• Its useful!
• Scientists and engineers, of course.
• But also
• Restaurant managers- How much fish do I need to
  order for the weekend?
• Business- What do we expect next quarters
  profits to look like?
• TV- Are enough people watching our show? Nielson
• Politics- Whos going to win the election?
• Medicine- Does this drug actually work?

3
What is statistics?

• Well try to make it a fun course.
• More about critical thinking than calculations.
• What is Statistics?
• One definition The science of drawing
  conclusions from data.
• Collection of methods to
• Display Data
• Summarize Data
• Compare Data
• Model Data
• A method to generalize from limited data (sample)
  to a larger population that has not been
  measured.
• The word also refers to a number calculated from
  data to summarize some aspect of the data.

4
Orange Juice

• 95 of kids prefer Matos Orange Juice!!
• Buy lots of it now!
• Got a problem with that?
• Missing information!
• Its easy to be misled by
• statistics, if you dont
• know what to watch for.

5
Nuts and Bolts

• Syllabus
• Grading Tests, Quizzes, etc
• MathXL
• Textbook
• Group work
• Website
• Office Hours
• Asking Questions
• 3 Strikes, Drop Day, other info?

6
Last bit about the course

• Youll experience and (hopefully) understand
  statistical analysis by working with real data,
  from many different fields.
• We will work on the process of
• Asking a question
• Gathering needed data
• Analyzing data
• Making conclusions
• The stress is on concepts, critical thinking,
  problem solving, not calculations.
• We will rarely calculations by hand- well use
  tools (DataDesk and calculators/MathCad) to do
  the number crunching.

7
Stages of the Class

• Data Analysis-
• forms our toolbox, methods to organize and
  describe data- graphs, numbers, etc.
• Data Production
• Where does the data come from? How do we get the
  data we need to answer a question?
• Statistical Inference
• What do the numbers tell me?
• How trustworthy is the data?

8
Chapter 2

• Data

9
What are Data?

• Data forms the foundation of statistics.
• So what, exactly, are data?
• Yes, thats grammatically correct.
• What do you think?
• Numbers or other information with a
  context/meaning.
• You should always be asking
• What do the data tell me?

10
Organization

• Catherine 33
• 69 7
• What does it mean?? Any thoughts?
• Lets add a little context through organization
• Name Height (inches) Age (yrs) in pocket
• Catherine 69 33 7
• This tells you a lot more. Dont know the whole
  context, but thats ok.

11
Vocabulary

• Statistics has its own vocabulary, and you need
  to learn to understand and use it.
• Data Set collection of information about
  individuals
• What constitutes an individual? Any ideas?
• People
• Objects
• Plants
• Animals, etc.
• Case Any individual about whom/which we have
  data.

12
Tables and variables

• Data sets need systematic organization.
• Students in 1231 class. What can you tell?

Case (each row)
Variable (each column)
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Whats a variable?

• ANY characteristic of an individual that can be
  measured/recorded.
• Name some possible variables

14
Filling in the Context

• Finding the 5 Ws will give us a fairly complete
  picture of the context of the data.
• Most critical to answer
• Who?
• Who is the data about?
• What individuals does the data describe? (i.e. 22
  statistics students)
• What?
• What are the variables measured?
• What do the variables mean? What are the units?

15
The rest of the context...

• When?
• When was the data taken?
• Ex heights from 1750 vs from 2005
• Where?
• Where was the data taken?
• Ex heights from China vs America
• Why?
• Why was the data collected?
• How?
• How was the data collected?
• Can effect usefulness
• 900 number poll?
• Important You might not be able to answer all of
  the 5 Ws. Investigate further (if possible) to
  find answers.

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5 Ws Example

• The Gallup Poll conducted a representative
  telephone survey of 1180 American voters during
  the first quarter of 1999. Among the reported
  results were the voters region (Northeast,
  South, etc), age, party affiliation, and whether
  or not the person had voted in the 1998 midterm
  Congressional election.
• ID the Ws
• Who
• What
• When
• Where
• Why
• How

1180 American voters
Region, age, party affiliation, whether voted
1st quarter 1999
America
for a Gallup Poll, but we cant infer much more
Telephone poll
Note The Variables are the What!
17
Kinds of Variables

• 2 Main kinds of variables that well cover
• Categorical
• Variable names categories
• Tells which of several groups/categories an
  individual belongs to
• Ex Gender
• Quantitative
• Has a NUMERICAL value
• Answers questions about the quantity of what is
  measured.
• Needs units!
• When you add, average, etc values, the results
  still make sense.
• Ex Age
• But also.
• Identifier variables- ID number, etc.
• Really a categorical variable with one individual
  in each category.
• Ordinal
• Report order (rate on scale of 1(disagree) to 5
  (agree) )
• Need to decide if Categorical or Quanitative
• We generally wont deal with these.

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Identify Cat Var or Q Var

• Job
• Income
• Region
• Zip Code
• Percent Profit
• Sorority
• Price
• SSN

19
MMs

• Open your bag of MMs.
• DO NOT EAT THEM YET!!
• Construct a question that needs a categorical
  variable.
• Think about your Who when you do this
• Construct a question that uses a quantitative
  variable.
• Gather that data from your bag.
• Share with class.

20
More MMs

• Class-
• Choose a color
• Count the number of each color in your bag.
• Count the total number of MMs in your bag
• Eat your MMs.

21
End of Chapter

• Read Chapter 3
• Work through ActivStats Ch 2 and 3.
• Log into MathXL. There is a homework already
  available.