Ch. 1 Stats Starts Here , Ch. 2 Summarizing Data & Describing Categorical Data (2.1)

What is statistics?

Way of reasoning, along with a collection of tools & methods designed to help us understand the world using data

What are the 3 different ways statistics can be used?

• Describe and present a particular situation

• Test competing claims/theories

• Make future predictions, etc

In a dataset, what are the individual cases?

the objects described by a set of data (what you are observing)

What are 3 examples of possible individual cases?

people, animals,things, etc

What is a variable?

any characteristic of an individual case (or individual)

Fill in the blank.

Variables can take _______ values on __________
cases.

different, different

Where is data usually organized?

in tables

In a table, with dataset provided…

what do the rows represent?

cases

In a table, with dataset provided…

what do the columns represent?

variables

In this image of this particular dataset…

what are the individuals and variables?

individuals : university students

variables : Name (idenitifer variable), DOB, Gender, Major, GPA

When planning a statistical study or exploring
data from someone else’s work, what are the 6 types of questions you should ask yourself?

Why, Who, What and How (and if possible When & Where)

What are the 2 types of variables?

1. categorical variable

2. quantitative variable

When planning a statistical study or exploring
data from someone else’s work, what are the “what” type of questions you should ask?

How many variables do the data contain?
Exact definitions of these variables? In what units
of measurement is each variable recorded?

When planning a statistical study or exploring
data from someone else’s work, what are the “why” type of questions you should ask?

What purpose do the data have? Do we
hope to answer some specific questions? Do we
want to draw conclusions about individuals other
than the ones actually have data for?

When planning a statistical study or exploring
data from someone else’s work, what are the “who” type of questions you should ask?

What cases (or individuals) do the data
describe? How many individuals are in the data?

When planning a statistical study or exploring
data from someone else’s work, what are the “how” type of questions you should ask?

How the data collected?

When planning a statistical study or exploring
data from someone else’s work, what are the “where&when” type of questions you should ask?

At what location & time did they collect the data?

What would be classified as “categorical variable”?

A variable that can place an individual case into one of several groups or categories

What would be classified as “quantitative variable”?

A variable that takes numerical values for which arithmetic operations are defined

True or false.

Height & GPA are classified as categorical variable.

False.

True or false.

Gender & Collage Major are classified as quantitative variables.

False. 

What are the two different types of categorical variables?

1. nominal - unordered categories

2. ordinal - ordered categories

True or false.

Patient condition: excellent, good, fair, poor is an example of an ordinal category variable.

True

What type of categorical variable does this example follow : Major: Mathematics, Statistics or Computer Science?

nominal

What are identifier variables?

categorical variables with exactly one individual in each category.

True or false.

You can analyze identifier variables.

False.

True or false.

Gender is a idenitifer variable.

False.

True or false.

SIN is an idenitifer variable.

True.

What are two ways, we can describe categorical data?

through using tables &charts

Answer the following :

 who (individual cases):
 what (variables):
 categorical:
 quantitative:
 why:
 when:
 where:
 how:

 who (individual cases): aircraft (flights)
 what (variables):
 categorical: type of aircraft, any mechanical problems (nominal-type of categorical variable) , flight # (identifier)
 quantitative: how late the flight was, # of passengers
 why: monitor customer safety and service
 when: ongoing
 where: worldwide
 how: all airlines report flights

What are 3 ways we can describe categorical data in tables?

1. frequency

2. relative frequency

3. contingency table

What are 3 ways we can describe categorical data in charts (visually)?

1. bar chart

2. pie chart

3. side-by-side chart

What are frequency table?

Tables that list all categories and their frequencies.

What do frequency tables describe?

Describes distribution of a categorical variable ( the values & how frequently they occur)

What kind of categorical table is this?

A frequncy table.

What is a relative frequency table?

A table that lists all categories and their relative frequencies.

How would you calculate the relative frequency of A given the frequency table?

Rel. freq. (%) of A = 40(frequency) / 200(total) × 100(% ; percentage) = 20%

What type of categorical table is this?

Relative frequency table

What is a bar chart?

It’s a chart where each category is represented by bars, (the height of each bar is considered to be the relative frequency)

What is a pie chart?

It’s a chart where the categories ate represented by a pie slices, where the size of each slice is proportional to relative frequency

Answer the following question provided on the image.

4,200

What should the distribution of categorical variables always add up to?

100% or 1 in probablity

When adding all values of relative frequency, they should all give you?

100%