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
(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
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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Types of Data
 Parameter vs. Statistic
 Quantitative Data vs. Qualitative Data
 Discrete Data vs. Continuous Data
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Definitions

a numerical measurement describing some characteristic of a population population parameter
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Definitions

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
2 3
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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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 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 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
 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
$40,000
$40,500
$40,000
$40,500
35,000 30,000
$24,400
30,000 20,000
$24,400
25,000 10,000
20,000
Bachelor High School
Degree Diploma
(a) (test question)
0
Bachelor High School
Degree Diploma
(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
 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
 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
 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

Factorial Notation
8! = 8x7x6x5x4x3x2x1

Order of Operations
1. ( )
2. POWERS
3. MULT. & DIV.
4. ADD & SUBT.
5. READ LIKE A BOOK

Keep number in calculator as long a possible
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