Chapter 1 Slides

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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
conclusions) about an entire population
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
Bad Samples
Small Samples
Loaded Questions
Misleading Graphs
Pictographs
Precise Numbers
Distorted Percentages
Partial Pictures
Deliberate Distortions
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Abuses of Statistics
Bad Samples
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.
Loaded Questions
Survey questions can be worked to elicit a desired
response
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Abuses of Statistics
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Bad Samples
Small Samples
Loaded Questions
Misleading Graphs
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
mislead by its general shape.
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Abuses of Statistics
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Bad Samples
Small Samples
Loaded Questions
Misleading Graphs
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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Bad Samples
Small Samples
Loaded Questions
Misleading Graphs
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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Bad Samples
Small Samples
Loaded Questions
Misleading Graphs
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
road.”
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
 Identify your objective
 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
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Factorial Notation
8! = 8x7x6x5x4x3x2x1
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Order of Operations
1.
2.
3.
4.
5.
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( )
POWERS
MULT. & DIV.
ADD & SUBT.
READ LIKE A BOOK
Keep number in calculator as long a possible
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