Transcript Document

Introduction To Statistics
Math 13
Essentials of
Statistics
3rd edition
by Mario F. Triola
Copyright © 2007 Pearson Education, Inc
Publishing as Pearson Addison-Wesley.
Chapter 1
Introduction to Statistics
1-1 Overview
1-2 Types of Data
1-3 Critical Thinking
1-4 Design of Experiments
Section 1-1
Overview
Copyright ©
2007 Pearson
Education, Inc
Publishing as
Pearson
Addison-
Overview
A common goal of studies and surveys is to
collect data from a small part of a larger group
so as to learn something about the larger
group.
That is what the science of statistics does: tells
us how to:
1) collect data with an appropriate sample;
2) organize, analyze, and describe it; and
3) make inferences about the entire
population based on the data collected.
You will learn about:
•Collecting data using different random
sampling techniques;
•Analyzing data by taking different
kinds of measurements of it to observe
a pattern or trend;
•Inferring a hypothesis from the
observed measurements;
•Verifying your hypothesis.
Definition
 Data
bits of information collected through
observations, measurements, survey
responses.

The set of the student heights, in inches, in our class is:
{66, 64, 72, 69, 85, …};

The set of the student voting preferences in our class is:
{democrat, democrat, republican, undecided,….}

Singular for ‘Data’ is Datum, or Data Element, or Data Value.
Definition
 Population
the complete collection of all elements
(scores, subjects, measurements, etc.) to be
studied; the collection is complete in the
sense that it includes all subjects to be
studied:
–
–
All American adults consume on average 20.5 lbs of
sugar per year.
All factory bearings have a lifetime warranty.
 Census
collection of data from every member of a
population.
–
–
Virtually impossible thing to do.
Very susceptive to errors.
Definition
 Sample
Sub-set of members selected from a
population:
–
A sample is easier to collect, but it must be random
in order to have any statistical significance.
–
The 1097 sampled adults consume on average 22
lbs of sugar per year.
Definition
 Parameter
measurement which describes the
Population:
–
In the statement “All American adults consume on
average 20.5 lbs of sugar per year”, the number 20.5
is a parameter.
 Statistic
measurement which describes the
Sample:
–
In the statement “the 1097 sampled adults consume
on average 22 lbs of sugar per year’, the number 22
is a statistic.
Definition
 Parameter
a number that describes the Population:
Population
parameter
 Statistic
a number that describes the Sample:
sample
statistic
Key Concepts
 Sample data must be representative
of the entire population, which means
it must be collected through a process
of random selection in order to enable
us to draw from this sample
conclusions about the population.
 If sample data are not collected in an
appropriate way, the data may be
completely useless and the methods of
statistics will not apply.
Key Concept
If sample data are collected in
an appropriate way, then we are
interested in using the sample
data to make inferences (or
generalizations) about the entire
population.
Section 1-2
Types of Data
Copyright ©
2007 Pearson
Education, Inc
Publishing as
Pearson
Addison-
DATA
Numerical
Discrete
Categorical
Continuous
Copyright ©
2007 Pearson
Education, Inc
Publishing as
Pearson
Addison-
Definition
 Numerical (Quantitative) data
are numbers representing counts or
measurements. It makes sense to find
the average of a set of numerical data:
–
–
–
The weights of students;
The number of cars per household;
The blood type (?)
Definition
Categorical (Qualitative) data
are symbols, names, numbers, letters
representing different categories. It makes NO
sense to find the average of a set of categorical
data:
–
–
–
The genders of students;
The color of cars;
The blood type.
DATA
Numerical
Discrete
Continuous
Numerical data can further
be described as discrete or
continuous.
Categorical
Definition

Discrete numerical data
come from observations that can only be
measured in a finite (or countable)
number of ways, each of which has a
clear boundary point on the number line
– counts:
–
–
–
the number of cars in a household;
the number of offspring an elephant produces;
the salary of an adult, to the nearest dollar;
Definition
 Continuous numerical data
come from observations that can be
measured in infinitely many possible values,
which can be viewed on a continuous scale
without gaps; each measurement has no
clear boundary with the next one –
measurements:
–
–
The amount of milk that a cow produces; e.g.
2.343115 gallons per day;
The student’s height, if not rounded off.
DATA
Numerical
Discrete
Continuous
Categorical
Levels of Measurement
Another way to classify data is to use
levels of measurement. There are
four of these levels:
1. Nominal
2. Ordinal
3. Interval
4. Ratio
Definition
 Nominal level of measurement
are data that consist of categories only.
Nominal data cannot be arranged in any
order (such as low to high)
–
–
–
–
Survey responses: yes, no, undecided
Blood type: A, B, AB, O
Car color: red, blue, silver, …
Gender: male or female
Definition
 Ordinal level of measurement
are data that can be arranged in some
order.
Ordinal data allow for relative comparison.
However differences between data values
cannot be determined or are meaningless –
difference comparison is impossible:
–
–
–
Course grades: A, B, C, D, or F
Class of a Hotel: 1st, 2nd, 3rd, …
Gender: male or female (?)
Definition
 Interval level of measurement
are data which can be arranged in some order,
with the additional property that the difference
between any two data values is meaningful.
Interval data allow for difference comparison.
However, there is no natural zero starting point,
which makes the ratio comparison impossible:
–
–
–
Year of a masterpiece: 1000, 2000, 1998, etc.
Body temperature: 101.2, 104.5, 103.0, …
Test score: 70%, 85%, 94%, 50% (?)
Definition
 Ratio level of measurement
is like the interval level with the additional
property that there is a natural zero starting
point (zero indicates that none of the
quantity is present), which makes ratio
comparisons also meaningful:
–
–
–
The price of a textbook: $100, $200, $120, …
The number of eggs a hen lays: 6, 12, 1, 0, …
The amount of milk a cow produces: 2.34, 3.11,
etc gallons per day
Summary - Levels of Measurement
 Nominal - categories only; no
comparison is possible;
 Ordinal - categories (or numbers
grouped in categories) arranged in order;
relative comparison only;
 Interval – numbers; relative and
difference comparison possible;
 Ratio – numbers; relative, difference
and ratio comparison possible.
Recap
In this section we have looked at:
 Basic definitions and terms describing data
 Parameters versus statistics
 Types of data (quantitative and qualitative)
 Levels of measurement
1. The population is
A. A collection of observations.
B. A collection of methods for planning
studies and experiments.
C. The complete collection of all elements.
D. A sub-collection of members drawn
from a larger group.
2. Which is an example of quantitative data?
A. Weights of high school students.
B. Genders of actors and actresses.
C. Colors of the rainbow.
D. Consumer ratings of a particular
automobile (below average, average, and
above average.)
3. Which is not an example of continuous
data?
A. Temperature on a thermometer.
B. Number of students in an algebra class.
C. Mean weight of 100 flour sacks.
D. Amount of water pumped from a pond per
day.
4. Questions on a survey are scored with
integers 1 thru 5 with 1 representing Strongly
Disagree and 5 Strongly Agree. This is an
example of what kind of measurement?
A. Nominal.
B. Ratio.
C. Ordinal.
D. Interval.
5. Identify the level of measurement: the
weights of people
A. Nominal.
B. Ordinal.
C. Interval.
D.Ratio.
6. Identify the level of measurement: a
movie critic’s classification of “drama”,
“comedy”, “adventure”, “science-fiction”
A. Nominal.
B. Ordinal.
C. Interval.
D.Ratio.
7. Identify the level of measurement of the
values “must see”, “recommend” and
“don’t even think about going” which a
movie critic is using to rate movies
A. Nominal.
B. Ordinal.
C. Interval.
D. Ratio.
ANSWER
The population is
A. A collection of observations.
B. A collection of methods for planning
studies and experiments.
C. The complete collection of all elements.
D. A sub-collection of members drawn
from a larger group.
The population is
A. A collection of observations.
B. A collection of methods for planning
studies and experiments.
C. The complete collection of all elements.
D. A sub-collection of members drawn
from a larger group.
Which is an example of quantitative data?
A. Weights of high school students.
B. Genders of actors and actresses.
C. Colors of the rainbow.
D. Consumer ratings of a particular
automobile (below average, average, and
above average.)
Which is an example of quantitative data?
A. Weights of high school students.
B. Genders of actors and actresses.
C. Colors of the rainbow.
D. Consumer ratings of a particular
automobile (below average, average, and
above average.)
Which is not an example of continuous data?
A. Temperature on a thermometer.
B. Number of students in an algebra class.
C. Mean weight of 100 flour sacks.
D. Amount of water pumped from a pond per
day.
Which is not an example of continuous data?
A. Temperature on a thermometer.
B. Number of students in an algebra class.
C. Mean weight of 100 flour sacks.
D. Amount of water pumped from a pond per
day.
Questions on a survey are scored with
integers 1 thru 5 with 1 representing Strongly
Disagree and 5 Strongly Agree. This is an
example of what kind of measurement?
A. Nominal.
B. Ratio.
C. Ordinal.
D. Interval.
Questions on a survey are scored with
integers 1 thru 5 with 1 representing Strongly
Disagree and 5 Strongly Agree. This is an
example of what kind of measurement?
A. Nominal.
B. Ratio.
C. Ordinal.
D. Interval.
Identify the level of measurement: the
weights of people
A. Nominal.
B. Ordinal.
C. Interval.
D.Ratio.
Identify the level of measurement of the
variable weight
A. Nominal.
B. Ordinal.
C. Interval.
D. Ratio.
Identify the level of measurement: a movie
critic’s classification of “drama”, “comedy”,
“adventure”, “science-fiction”
A. Nominal.
B. Ordinal.
C. Interval.
D. Ratio.
Identify the level of measurement: a movie
critic’s classification of “drama”,
“comedy”, “adventure”, “science-fiction”
A. Nominal.
B. Ordinal.
C. Interval.
D.Ratio.
Identify the level of measurement of the
values “must see”, “recommend” and
“don’t even think about going” which a
movie critic is using to rate movies
A. Nominal.
B. Ordinal.
C. Interval.
D.Ratio.
Identify the level of measurement: a movie
critic’s rating of “must see”, “recommend”,
“don’t even think about going”
A. Nominal.
B. Ordinal.
C. Interval.
D.Ratio.
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