1. Elementary Statistics
Math 1342

2. Chapter 1
The Nature of Probability and Statistics
• 1-1 Descriptive and Inference Statistics
• 1-2 Variables and Types of Data
• 1-3 Data Collection and Sampling Techniques
• 1-4 Observational and Experimental Studies
• 1-5 Uses and Misuses of Statistics
• 1-6 Computers and Calculators

3. 1-1 Introduction
Statistics is the science of conducting studies to
collect, organize, analyze, and draw conclusions from data.

4. 1-1 Descriptive and Inference Statistics
Descriptive Statistics consists of the
collection, organization, summarization, and presentation of data.
Inferential Statistics consists of generalizing from samples to
populations, performing estimations and hypothesis
tests, determining relationships among variables, and making
predictions.

5. 1-1 Descriptive and Inference Statistics
A Variable is a characteristic or attribute that can assume different
values.
Data are the values (measurements or observations) that the
variables can assume.
A collection of data values forms a data set. Each value in the data set
is called a data value or datum.
A population consists of all subjects (human or otherwise) that are
being studied.
A sample is a group of subjects selected from a population.

6. 1-2 Variables and Types of Data
Variables can be classified as qualitative and quantitative.
Qualitative variables are variables that can be placed into distinct
categories, according to some characteristic or attribute.
For example, a variable of gender (male or female)
Quantitative variables are numerical and can be ordered and ranked.
For example, a variable age. (17, 22, 80, etc)
Discrete variables assume values that can be counted.
Continuous variables can assume an infinite number of values
between any two specific values. They are obtain by measuring.

7. 1-3 Variables and Types of Data
Levels of Measure:
Nominal
Classifies data into mutually exclusive (non-overlapping) exhausting
categories in which no order or ranking can be imposed on the data.
Example 1: Teachers classified according to subject
(Math, English, History, etc.)
Example 2: Classify according to zip codes
Example 3: Classify according to marital status
(single, married, divorced, widowed, separated)
Ordinal
Classifies data into categories that can be ranked; however, precise
differences between the ranks do not exist.
Example 1: Student evaluations (superior, average, or poor)
Example 2: Letter grades (A, B, C, D)

8. 1-3 Variables and Types of Data
Levels of Measure:
Interval
Ranks data, and precise differences between units of measure exists.
No meaningful zero.
Example: IQ Test (There is a precise difference between an IQ
of 109 and an IQ of 110 but an IQ test does not measure people
with no intelligence)
Ratio
Possesses all the characteristics of interval measurement, and there
exists a true zero.
Example: measure of height, weight, area, and number of
phone calls received.

9. 1-3 Data Collection and Sampling
Random
Subjects are selected by random numbers.
Systematic
Subjects are selected by using kth number after the first subjects is
randomly selected from 1 through k.
Stratified
Subjects are selected by dividing up the population into groups
(strata), and subjects within groups are randomly selected.
Cluster
Subjects are selected by using an intact group that is representative of
the population.

10. 1-4 Observational and Experimental
Studies
Observational study
Researcher merely observes what is happening or what has happened
in the past and tries to draw conclusions based on these observations.
Experimental study
Researcher manipulates one or two variables and tries to determine
how the manipulation influences other variables.
Independent variable
In an experimental study, Independent variable is the one that is
being manipulated by the researcher. The resulting variable is called
Dependent variable.
Confounding variable is the one that influences the dependent or
outcome variable but can not be separated from the independent
variable.

11. 1-5 Uses and Misuses of Statistics
“These are three types of lies……lies, damn
lies, and statistics”
“Figures don’t lie, but liars figure”
Here are some ways that statistics can be
misrepresented:
•Suspect Samples … the size of the sample … how was the
sample selected
•Ambiguous Averages … median … mode … midrange
•Changing the Subject … what is better to hear, 3% or
$6,000,000, when both are correct?
•Detached Statistics … Our brand of crackers has one-third
fewer calories.
•Implied Connections
•Misleading Graphs
•Faulty Survey Questions

12. 1-6 Uses and Misuses of Statistics
•Implied Connections … Eating fish may help to reduce your
cholesterol
•Misleading Graphs … drawn inappropriately.
•Faulty Survey Questions … For a survey, should the question
be: “Do you feel that San Benito CISD should build a new
football stadium?” or “Do you favor increasing school taxes so
San Benito CISD can build a new stadium?”

13. Lecture Notes 1
1. Descriptive and inferential statistics. Descriptive describes a
set of data. Inferential statistics uses a set of data to make
predictions about populations.
2. Probability deals with events that occur by chance. It is used
in insurance and gambling.
3. Gambling, insurance, education, etc.
4. A population is the totality of all subjects under the study. A
sample is a subgroup of the population.
5. When the population is large, the researcher saves time and
money using samples.

14. Lecture Notes 1
6.
a) Inferential
b) Descriptive
c) Descriptive
d) Descriptive
e) Inferential
f) Inferential
g) Descriptive
h) Inferential

15. Lecture Notes 1
7.
a) Ratio
b) Ordinal
c) Ratio
d) Interval
e) Ratio
f) Ordinal
g) Ratio
h) Ratio
i) Nominal
j) Ratio

16. Lecture Notes 1
8.
a) Quantitative
b) Qualitative
c) Quantitative
d) Quantitative
e) Qualitative
f) Quantitative
g) Qualitative

17. Lecture Notes 1
9.
a) Discrete
b) Continuous
c) Continuous
d) Continuous
e) Discrete
f) Discrete
g) Continuous

18. Lecture Notes 1
10.
a) 42.75-42.85
b) 1.55-1.65
c) 5.355-5.365
d) 17.5-18.5
e) 93.75-93.85
f) 39.5-40.5

19. Lecture Notes 1
11. Random, systematic, stratified, cluster.
12.
a) Cluster
b) Systematic
c) Random
d) Systematic
e) Stratified