Transcript Section 3.1 Beyond Numbers What Does Infinity Mean?

Section 8.1
Stumbling Through A Minefield of Data
Inspiring Statistical Concepts Through Pitfalls
A picture is worth a thousand words – unless the
picture is distorted.
Question of the Day
Would you answer the following question
honestly in public:
Have you been drunk in the past 48 hours?
Graphically distorted data
Graphically distorted data
Collecting Data
Leading and misleading data
Surveys can produce skewed results by
phrasing the questions in ways that might bias
the answers.
Collecting Data
Sample Bias – Polluted Pools
The answers we get often depend on whom we
ask.
Collecting Data
Where could bias occur in every day life?
Collecting Data
Are we asking the right question?
1. What is the question?
2. What role will the data play in answering that
question?
Section 8.2
Getting Your Data to Shape Up
Organizing, Describing, and Summarizing Data
Search for the most effective
means of making your case.
Question of the Day
What do these numbers have in common:
3.23, 0.360, 82, 1.08, 2,500,000.
Visualizing Data
Pie Charts
Visualizing Data
Stem and Leaf Plot
Visualizing Data
Histogram
Summarizing Data
Measures of Center (Averages)
Mean – the sum of all the numerical data
divided by the number of data points.
Median – the middle data point when the
data are lined up in numerical order.
Measuring Variation
Measuring Variation
Five-Number Summary:
Minimum Value
First Quartile
Second Quartile (Median)
Third Quartile
Maximum Value
Measuring Spread
Standard Deviation – a measure of how far the
average data point differs (or deviates) from the
mean.
The Shape of Graphs
Skewed graphs
The Shape of Graphs
Bimodal Distributions
Section 8.3
Looking at Super Models
Mathematically Described Distributions
All models are wrong.
Some are useful.
George E. P. Box
Question of the Day
Who was a better batter: Joe Jackson or
Moises Alou?
Uniform Distributions
Normal Distributions
The Bell Curve
Normal Curves and Standard Deviation
Section 8.4
Go Figure
Making Inference from Data
If the going gets tough, do something else.
Question of the Day
If you flip a coin 100 times and see heads
only 41 times, how confident are you that
your coin is fair?
The Ideas Behind Statistical Inference
Setting 1:
There exists a fixed collection of data, but
we only know a sample of it. Our goal is to
infer the data of the entire population from
analyzing that sample.
The Ideas Behind Statistical Inference
Setting 2:
Some fact about reality is unknown, and so
we employ statistical analyses to help us
determine what is most likely true.
The Ideas Behind Statistical Inference
Setting 3:
Reality contains some probabilistic feature
and we use a random sample to determine
what the chances are.
Confidence Intervals
“Poll shows that Arnold Schwarzenegger will
receive 46% of the vote with a  3%
margin of error.”
What does that statement mean?
When is enough enough?
The sample size is more important than the
sample’s percentage of the overall
population.
For 95% confidence, a sample size n will
1
have a margin of error of approximately
n
Section 8.5
War, Sports, and Tigers
Statistics Throughout Our Lives
Whenever possible, create an experiment
and study the outcomes.
Question of the Day
Is every possible number equally likely in a
lottery?
The Birth of Genetics
Examining data can drawing conclusions
from it can have profound consequences.
Relationships versus
Cause and Effect
When we observe that two quantities vary in
a related manner, it is natural to wonder if
one is the cause of the other.
BEWARE!
Measuring Relationships
Correlation – the extent to which a
relationship exists.