1-1 overview 1- 2 types of data 1- 3 abuses of statistics 1- 4design of experiments
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1-1 Overview
1- 2 Types of Data
1- 3 Abuses of Statistics
1- 4 Design of Experiments
Chapter 1 Introduction to Statistics
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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
1-1 Overview
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Definitions
Population The complete collection of all
data to be studied.
SampleThe subcollection data drawn from the population.
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ExampleIdentify the population and
sample in the studyA quality-control manager randomly selects 50 bottles of Coca-Cola to assess the calibration of the filing machine.
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Statistics
Broken into 2 areas
Descriptive Statistics Inferencial Statistics
Definitions
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DefinitionsDescriptive 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 QuestionTest Question
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Parameter vs. Statistic
Quantitative Data vs. Qualitative Data
Discrete Data vs. Continuous Data
1-2 Types of Data
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Parameter
a numerical measurement describing some characteristic of a population
population
parameter
Definitions
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Statistic
a numerical measurement describing some characteristic of a sample
sample
statistic
Definitions
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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) dataCan 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) dataThe eye color of FLC students
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We further describe quantitative data by
distinguishing between discrete and
continuous data
Definitions
Quantitative Quantitative DataData
DiscreteDiscrete
ContinuousContinuous
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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
Definitions
2 3
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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.
Examples
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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
Definitions
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Univariate Data How many first year students attend FLC?
Bivariate DataIs there a relationship between then number of
females in Computer Programming and their scores in Mathematics?
Example
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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
Important Characteristics of Data
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Uses of Statistics
Almost all fields of study benefit from the application of statistical methodsSociology, Genetics, Insurance, Biology, Polling,
Retirement Planning, automobile fatality rates, and many more too numerous to mention.
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Bad Samples Small Samples Loaded Questions Misleading Graphs Pictographs Precise Numbers Distorted Percentages Partial Pictures Deliberate Distortions
1-3 Abuses of Statistics
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Abuses of StatisticsBad 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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Bad Samples Small Samples Loaded Questions Misleading Graphs Pictographs Precise Numbers Distorted Percentages Partial Pictures Deliberate Distortions
Abuses of Statistics
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Bachelor High SchoolDegree Diploma
Salaries of People with Bachelor’s Degrees and with High School Diplomas
$40,000
30,000
25,000
20,000
$40,500
$24,400
35,000
$40,000
20,000
10,000
0
$40,500
$24,40030,000
Bachelor High SchoolDegree Diploma
(a) (b)(test question)
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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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Bad Samples Small Samples Loaded Questions Misleading Graphs Pictographs Precise Numbers Distorted Percentages Partial Pictures Deliberate Distortions
Abuses of Statistics
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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 What is actually intended here? 2 intended here? 2 times or 8 times?times or 8 times?
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Bad Samples Small Samples Loaded Questions Misleading Graphs Pictographs Precise Numbers Distorted Percentages Partial Pictures Deliberate Distortions
Abuses of Statistics
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Precise NumbersThere 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
Abuses of Statistics
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Bad Samples Small Samples Loaded Questions Misleading Graphs Pictographs Precise Numbers Distorted Percentages Partial Pictures Deliberate Distortions
Abuses of Statistics
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Abuses of StatisticsPartial 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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Experiment apply some treatment (Action)
Eventobserve its effects on the subject(s) (Observe)
Example: Experiment: Toss a coin
Event: Observe a tail
Definition
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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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Random (type discussed in this class)
Systematic
Convenience
Stratified
Cluster
Methods of Sampling
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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
Definitions
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Random Sampling - selection so that
each has an equal chance of being selected
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Systematic SamplingSelect some starting point and then
select every K th element in the population
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Convenience Samplinguse results that are easy to get
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Stratified Samplingsubdivide 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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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).
Definitions
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Factorial Notation 8! = 8x7x6x5x4x3x2x1
Order of Operations 1. ( )2. POWERS3. MULT. & DIV.4. ADD & SUBT.5. READ LIKE A BOOK
Keep number in calculator as long a possible
Using Formulas
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