Download - Chapter 1
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Quote of the Day
Oh, people can come up with statistics to prove anything. 14% of people know that. ---Homer Simpson
What are Statistics?
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Chapter 1:The Nature of Probability and Statistics
Section 1:Descriptive and Inferential
Statistics
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Stats in Daily Life Of the people in the US, 14% said they
feel happiest in June, and 14% said they feel happiest in December.
The average in-state college tuition and fees for 4-year pubic college is $5,836.
Every day in the US about 120 golfers claim that they made a hole-in-one.
4 out of 5 doctors leaves one doctor.- Chevy Chase
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What is Statistics? The science of conducting studies to
collect, organize, summarize, analyze and draw conclusions from data.
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What is Data?
The values that the variables can assume.
A collection of values forms a Data Set Each Value in the data set is called:
Data Value or Datum
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What is a variable?
A characteristic or attribute that can assume different values.
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Types of Statistics
1. Descriptive Statistics Consists of the collection, organization,
summarization, and presentation of data Ex: Government Census
Taken every ten years Describes average income, family size, etc..
What does this mean? Basically used to describe a situation.
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Types of Statistics
2. Inferential Statistics Consists of generalizing from samples to
populations, performing estimations and hypothesis tests, determining relationships among variables, and making predictions.
Ex: Winning the lottery 1 in a million
What does this mean ? Used to predict the outcome of an event.
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What is the difference between a Population and a Sample?
Population- consists of all subjects that are being studied.
Sample- is a group selected from a population.
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Population Sample
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Assignment
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Section 2: Types of Variables
Qualitative Variables: Variables that can be placed into
distinct categories, according to some characteristic or attribute.
Ex: Gender, Eye color, Geographic Location
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2 Types of Variables
Quantitative Variables: Variables that are numerical and can
be ordered or ranked. Ex: Age, height, weight, body temp Classified by two groups
Discrete Variables Continuous Variables
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Practice
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Discrete Variables
Assume values that can be counted
Assigned numbers such as 0,1,2,3,…
Ex: # of children # of students
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Continuous Variables Can assume an infinite number of
values between any two specific values.
Obtained by measuring Often include fractions and decimals. Ex:
Temperature Time Length
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Practice
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Measurement Scale
Used to categorize, count, or measure variables.
Types: Nominal Ordinal Interval Ratio
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Nominal Level of Measurement
Classifies data into mutually exclusive, exhausting categories in which no order or ranking can be imposed on the data.
Ex: Male/Female Single/Married/Divorced/Widowed/Separated Democratic/Republican
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Ordinal Level of Measurement Classifies data into categories that
can be ranked; however, precise differences between the ranks do not exist.
Ex: Letter Grades (A, B, C, D, F) 1st, 2nd, 3rd, etc Small, Medium, Large Freshman, Sophomores, Juniors, Seniors
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Interval Level of Measurement Ranks data, and precise differences
between units of measures do exist: however, there is no meaningful zero.
Ex: Temperature: 72°F and 73°F, difference
of 1°F, but 0°F does not mean no heat present
IQ: 109 and 110, difference of 1 point, but 0 does not mean there is no intelligence.
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Ratio Level of Measurement Possesses all the characteristics of
interval measurements, and there exists a true zero.
In addition, true ratios exists when the same variables is measured on two different members of the population.
Ex: Salary Time Age
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Practice
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Section 3: Data Collection and Sampling Techniques.
Types: Random Systematic Stratified Cluster
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Random Sampling
Selection based on chance or random numbers.
Procedure: Assign number to each subject in
population Select numbers at random from “hat”
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Random Sampling
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Systematic Sampling
Procedure: Number each subject in population Select every kth subject
Example: Population: 100 Sample: 10 Kth term: 100/10=10 1, 11, 21, 31, 41, 51, 61, 71, 81, 91
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Systematic SamplingPopulation: 21 Sample: 721/7=3: kth term is 3.
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Stratified Sampling
Procedures: Population divided into groups called:
Strata Groups have common characteristic
needed for study. Samples randomly selected from each
strata
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Stratified Sampling
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Cluster Sampling
Population is divided into groups called: Clusters
Select some clusters Survey every member of the
cluster for sample
Used with large populations
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Cluster Sampling
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Other sampling methods
Convenience sampling Use subjects that are convent Ex: asking people as they enter the
mall Sequential sampling Double sampling Multistage sampling
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Convenience Sampling
Do you want to take a survey?
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Practice
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Section 4: 2 Types of Studies
Observational Study Researchers merely observe what is
happening or what has happened in the past
Try to draw conclusions based on these observations.
Ex: studying creatures in the wild “Meerkat Manor”
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Experimental study Researchers manipulate one of the
variables Tries to determine how to the
manipulation influences other variables.
Ex: New medication and placebos
Section 4: 2 Types of Studies
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Practice
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Statistical Studies include…. Independent variables
In an experimental study is the one that is being manipulated by the researcher.
Also called: Explanatory variable
Dependent variables Resultant variable Also called: Outcome variable
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Misuses of Statistics Suspect Samples
Too small Convenience Volunteers
Changing the subject Increase of 3% Increase of $600,000
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Detached Statistics- no comparison “Works 5 times faster” “1/3 fewer calories”
Implied Connection “Eating fish may help you achieve
better in school”
Misuses of Statistics
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Misleading Graphs- Chapter 2
Faulty Survey Questions “Do you feel there should be a 4 day
school week?” “Do you feel there should be a 4 day
school week from 4 am to midnight?”
Misuses of Statistics
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Section 1-6: Computers and Calculators
Computer and Calculators GOOD
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End of Chapter 1