### Chapter 1 Slides

```Chapter 1
Introduction to Statistics
1-1 Overview
1- 2 Types of Data
1- 3 Abuses of Statistics
1- 4 Design of Experiments
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1-1
Overview
Statistics (Definition)
A collection of methods for planning
experiments, obtaining data, and then
organizing, summarizing, presenting,
analyzing, interpreting, and drawing
conclusions based on the data
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Definitions
Population
The complete collection of all
data to be studied.
Sample
The subcollection data drawn from
the population.
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Example
Identify the population and
sample in the study
A quality-control manager randomly selects 50
bottles of Coca-Cola to assess the calibration of
the filing machine.
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Definitions
Statistics
Broken into 2 areas
 Descriptive Statistics
 Inferencial Statistics
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Definitions
Descriptive Statistics
Describes data usually through the use of graphs,
charts and pictures. Simple calculations like mean,
range, mode, etc., may also be used.
Inferencial Statistics
Uses sample data to make inferences (draw
Test Question
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1-2
Types of Data
Parameter vs. Statistic
Quantitative Data vs. Qualitative Data
Discrete Data vs. Continuous Data
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Definitions
 Parameter
a numerical measurement describing
some characteristic of a population
population
parameter
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Definitions
Statistic
a numerical measurement describing
some characteristic of a sample
sample
statistic
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Examples
Parameter
51% of the entire population of the US is
Female
 Statistic
Based on a sample from the US population
is was determined that 35% consider
themselves overweight.
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Definitions
Quantitative data
Numbers representing counts or
measurements
 Qualitative (or categorical or
attribute) data
Can be separated into different categories
that are distinguished by some nonnumeric
characteristics
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Examples
Quantitative data
The number of FLC students with blue eyes
 Qualitative (or categorical or
attribute) data
The eye color of FLC students
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Definitions
We further describe quantitative data by
distinguishing between discrete and
continuous data
Discrete
Quantitative
Data
Continuous
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Definitions
Discrete
data result when the number of possible values is
either a finite number or a ‘countable’ number of
possible values
0, 1, 2, 3, . . .
 Continuous
(numerical) data result from infinitely many possible
values that correspond to some continuous scale or
interval that covers a range of values without gaps,
interruptions, or jumps
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Examples
Discrete
The number of eggs that hens lay; for
example, 3 eggs a day.
 Continuous
The amounts of milk that cows produce;
for example, 2.343115 gallons a day.
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Definitions
Univariate Data
» Involves the use of one variable (X)
» Does not deal with causes and relationship
 Bivariate Data
» Involves the use of two variables (X and Y)
» Deals with causes and relationships
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Example
Univariate Data
How many first year students attend FLC?
 Bivariate Data
Is there a relationship between then number of
females in Computer Programming and their
scores in Mathematics?
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Important Characteristics of Data
1. Center: A representative or average value that indicates
where the middle of the data set is located
2. Variation: A measure of the amount that the values vary
among themselves or how data is dispersed
3. Distribution: The nature or shape of the distribution of data
(such as bell-shaped, uniform, or skewed)
4. Outliers: Sample values that lie very far away from the vast
majority of other sample values
5. Time: Changing characteristics of the data over time
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Uses of Statistics
 Almost
all fields of study benefit
from the application of statistical
methods
Sociology, Genetics, Insurance, Biology, Polling,
Retirement Planning, automobile fatality rates, and
many more too numerous to mention.
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1-3
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Abuses of Statistics
Small Samples
Pictographs
Precise Numbers
Distorted Percentages
Partial Pictures
Deliberate Distortions
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Abuses of Statistics
Inappropriate methods to collect data. BIAS (on test)
Example: using phone books to sample data.
Small Samples (will have example on exam)
We will talk about same size later in the course.
Even large samples can be bad samples.
Survey questions can be worked to elicit a desired
response
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Abuses of Statistics
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Small Samples
Pictographs
Precise Numbers
Distorted Percentages
Partial Pictures
Deliberate Distortions
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Salaries of People with Bachelor’s Degrees and with High School
Diplomas
\$40,500
\$40,500
\$40,000
\$40,000
35,000
30,000
30,000
20,000
\$24,400
25,000
\$24,400
10,000
20,000
0
Bachelor High School
Degree Diploma
(a)
Bachelor High School
Degree Diploma
(test question)
(b)
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We should analyze the
numerical information given
in the graph instead of being
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Abuses of Statistics
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Small Samples
Pictographs
Precise Numbers
Distorted Percentages
Partial Pictures
Deliberate Distortions
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Double the length, width, and height of a cube,
and the volume increases by a factor of eight
What is actually
intended here? 2
times or 8 times?
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Abuses of Statistics
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Small Samples
Pictographs
Precise Numbers
Distorted Percentages
Partial Pictures
Deliberate Distortions
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Abuses of Statistics
 Precise Numbers
There are 103,215,027 households in the
US. This is actually an estimate and it
would be best to say there are about 103
million households.
Distorted Percentages
100% improvement doesn’t mean
perfect.
Deliberate Distortions
Lies, Lies, all Lies
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Abuses of Statistics
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Small Samples
Pictographs
Precise Numbers
Distorted Percentages
Partial Pictures
Deliberate Distortions
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Abuses of Statistics
Partial Pictures
“Ninety percent of all our cars sold in this
country in the last 10 years are still on the
Problem: What if the 90% were sold in the
last 3 years?
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1-4
Design of Experiments
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Definition
 Experiment
apply some treatment (Action)
 Event
observe its effects on the subject(s) (Observe)
Example: Experiment: Toss a coin
Event: Observe a tail
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Designing an Experiment
 Collect sample data
 Use a random procedure that avoids bias
 Analyze the data and form conclusions
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Methods of Sampling
 Random (type discussed in this class)
 Systematic
 Convenience
 Stratified
 Cluster
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Definitions
 Random Sample
members of the population are selected in
such a way that each has an equal chance of
being selected (if not then sample is biased)
 Simple Random Sample (of size n)
subjects selected in such a way that every
possible sample of size n has the same
chance of being chosen
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Random Sampling - selection so that
each has an equal chance of being selected
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Systematic Sampling
Select some starting point and then
select every K th element in the population
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Convenience Sampling
use results that are easy to get
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Stratified Sampling
subdivide the population into at
least two different subgroups that share the same
characteristics, then draw a sample from each
subgroup (or stratum)
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Cluster Sampling - divide the population
into sections (or clusters); randomly select some of
those clusters; choose all members from selected
clusters
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Definitions
 Sampling Error
the difference between a sample result and the true
population result; such an error results from chance
sample fluctuations.
 Nonsampling Error
sample data that are incorrectly collected, recorded, or
analyzed (such as by selecting a biased sample, using a
defective instrument, or copying the data incorrectly).
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Using Formulas

Factorial Notation
8! = 8x7x6x5x4x3x2x1
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Order of Operations
1.
2.
3.
4.
5.
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( )
POWERS
MULT. & DIV.