Statistics: Chapter 1
The Nature of Probability and Statistics
Section 1-1:
Descriptive and
Inferential Statistics
Learning Targets:
I will be able to demonstrate knowledge
of statistical terms.
 I will be able to differentiate between the
2 branches of statistics.

Vocabulary






Statistics
Variable
Data
Random variable
Data set
Descriptive Statistics





Inferential Statistics
Probability
Population
Sample
Hypothesis Testing
Statistics
 The
science of conducting
studies to collect, organize,
summarize, analyze, and draw
conclusions from data.
Reasons to Study Statistics
1.
2.
3.
To be able to read and understand the
various studies performed in your field.
You might be called on to conduct
research in your field.
You can use the knowledge to become
better citizens and consumers.
Variables and Data
Variable – a characteristic or attribute that
can assume different values
 Data – values that the variable assumes
 Random variable – variables whose values
are determined by chance
 Data set – a collection of data values

*Each value in the data set is called a data
value or datum.
Descriptive Statistics


Inferential Statistics
The collection, organization,
summarization, and
presentation of data.
Example: census results

◦ Info – age, income


◦ Collect – survey
◦ Organize
◦ Summarize

Generalizing of samples to
populations
Performing estimations and
hypothesis tests
Determine relationships
among variables
Making predictions
◦ Present – graphs, charts, tables
The 2 Branches of Statistics
Vocabulary for Inferential Stats
Probability – the chance of something
happening
 Population – all subjects being studied
 Sample – a group of subjects selected
from the population
 Hypothesis testing – decision making
process for evaluating claims about a
population, based on information
obtained from samples

APPLYING THE
CONCEPTS 1-1
Answers to
Applying the Concepts 1-1
The variables are grades and attendance.
The data consists of specific grades and
attendance numbers.
3. These are descriptive statistics.
4. The population under study is students at
Manatee Community College.
5. While not specific, we probably have data
from a sample of MCC students.
6. Based on the data, it appears that, in
general, the better your attendance the
higher your grade.
1.
2.
Section 1-2
Variables and Types of Data
Learning Targets
3. I will be able to identify types of data.
4. I will be able to identify the measurement
level for each variable.
Types of Data

Qualitative vs. Quantitative

Discrete vs. Continuous
Qualitative vs. Quantitative

Qualitative
◦ Variables that can be
placed in distinct
categories based on
characteristics or
attributes
◦ Examples:
 Gender
 Eye color

Quantitative
◦ Variables that have
numerical values and
can be ordered or
ranked
◦ Two types:
 Discrete
 Continuous
◦ Examples:
 Age
 Height
 Weight
Discrete vs. Continuous

Discrete – variables that can be counted
◦ Whole numbers
◦ Examples: number of children, number of
phone calls

Continuous – variables that cannot be
counted
◦ Need to be measured
◦ Fractions or decimals
◦ Examples: length, time, temperature
Continuous Variables (cont’)
Since continuous variables are measured
we round the data due to limits of the
measuring device, therefore continuous
variables have boundaries.
 Boundaries of 72 are written as 72.5 –
73.5. This means that the interval contains
values of 72.5 up to but not including
73.5. The value 73.5 will be in the next
interval.

Boundaries

Boundaries are given one additional
decimal place and always end in 5.
Variable
Recorded Value
Boundaries
Length
15 centimeters
14.5 – 15.5 centimeters
Temperature
86 degrees
85.5 – 86.5 degrees
Time
0.43 seconds
0.425 – 0.435 seconds
Mass
1.6 grams
1.55 – 1.65 grams
Measurement Levels of Variables

Nominal

◦ Categories with no
order or rank

◦ Categories can be
ranked with a precise
difference but no
meaningful zero
Ordinal
◦ Categories that can be
ranked, precise
differences between
ranks do not exist
Interval

Ratio
◦ Categories can be
ranked with a precise
difference and a
meaningful zero does
exist
Examples of Measurement Scales
Nominal
Ordinal
Interval
Ratio
Zip code
Grade
SAT score
Height
Gender
Judging
IQ
Weight
Eye Color
Rating Scale
Temperature
Time
Political Affiliation Ranking of Tennis
Players
Salary
Religious
Affiliation
Age
Major Field
Nationality
APPLYING THE
CONCEPTS 1-2
Answers to
Applying the Concepts 1-2
1.
2.
3.
4.
5.
6.
7.
Variables – industry and job-related
injuries
Industry – qualitative, injuries –
quantitative
Injuries – discrete
Industry is nominal, injuries is ratio
Railroads employ fewer people
Convenience, cost, service, etc.
Answers will vary.
Section 1-3:
Data Collection and
Sampling Techniques
Learning Target
5. I will be able to identify the four basic
sampling techniques.
Ways to collect data
Telephone survey
 Mailed questionnaire survey
 Personal interview survey
 Surveying records
 Observation

Pros?
 Cons?

4 Sampling Techniques
1.
2.
3.
4.
Random Sampling
Systematic Sampling
Stratified Sampling
Cluster Sampling
Random Sampling
Systematic Sampling
 Selected
 Number
by using
chance or random
numbers
 Use a random
number table
each
subject of the
population and then
select every kth
subject
 Divide
the
population into
groups (strata)
according to some
characteristic that is
important in the
study, then sampling
from each group
Stratified Sampling
 Divide
the population
into groups (clusters)
by some means such
as geographic area,
then randomly
choose clusters and
use every member of
those clusters.
Cluster Sampling
Other Sampling Method

Convenience sample – choosing subjects
that are convenient
APPLYING THE
CONCEPTS 1-3
Section 1-4:
Observational and
Experimental Studies
Learning Target:
6. I will be able to explain the
difference between an
observational and experimental
study.
OBSERVATIONAL STUDY
Researcher observes what is happening or
what has happened and tries to draw
conclusions based on those observations
 Example:

◦ Motorcycle Industry Council
◦ “Motorcycle owners are getting older and richer”
◦ Data was collected from 1990 and 1998 and
compared
◦ Considerable difference in age and income was
found
Experimental Study

Researcher
manipulates one of
the variables and
tries to determine
how the
manipulation
influences other
variables
Vocabulary for Experimental Studies

Independent variable the one being
manipulated

Treatment group –
group that receives
special instructions or
treatment

Control group – no
special treatments or
instructions
◦ (explanatory variable)

Dependent variable –
the resultant variable
◦ (outcome variable)
Confounding variable – influences the
dependent variable without being
separate from the independent variable
APPLYING THE
CONCEPTS 1-4
Answers to
Applying the Concepts 1-4
1.
2.
3.
4.
5.
6.
Experiment
Independent – chewed tobacco or not
dependent – blood pressure and heart
rate
Treatment group – tobacco, other group
was control
Answers will vary.
Answers will vary.
Answers will vary.
Section 1-5:
Uses and Misuses of
Statistics
“There are three types of lies – lies,
damn lies, and statistics”
“Figures don’t lie, but liars figure”
Misuses of Statistics
1.
2.
3.
4.
5.
6.
7.
Suspect Samples
Ambiguous Averages
Changing the Subject
Detached Statistics
Implied Connections
Misleading Graphs
Faulty Survey Questions
Section 1-6:
Computers and Calculators