Download - Section 8.1 Stumbling Through A Minefield of Data Inspiring Statistical Concepts Through Pitfalls
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Section 8.1Stumbling Through A Minefield of Data
Inspiring Statistical Concepts Through Pitfalls
A picture is worth a thousand words – unless the picture is distorted.
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Question of the Day
Would you answer the following questionhonestly in public:
Have you been drunk in the past 48 hours?
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Graphically distorted data
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Graphically distorted data
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Collecting Data
Leading and misleading dataSurveys can produce skewed results by phrasing the questions in ways that might bias the answers.
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Collecting Data
Sample Bias – Polluted PoolsThe answers we get often depend on whom we ask.
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Collecting Data
Where could bias occur in every day life?
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Collecting Data
Are we asking the right question?1.What is the question?2.What role will the data play in answering that
question?
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Section 8.2Getting Your Data to Shape Up
Organizing, Describing, and Summarizing Data
Search for the most effectivemeans of making your case.
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Question of the Day
What do these numbers have in common:
3.23, 0.360, 82, 1.08, 2,500,000.
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Visualizing Data
Pie Charts
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Visualizing DataStem and Leaf Plot
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Visualizing Data
Histogram
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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.
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Measuring Variation
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Measuring Variation
Five-Number Summary:Minimum ValueFirst QuartileSecond Quartile (Median)Third QuartileMaximum Value
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Measuring Spread
Standard Deviation – a measure of how far the average data point differs (or deviates) from the mean.
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The Shape of Graphs
Skewed graphs
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The Shape of Graphs
Bimodal Distributions
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Section 8.3Looking at Super Models
Mathematically Described Distributions
All models are wrong. Some are useful.
George E. P. Box
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Question of the Day
Who was a better batter: Joe Jackson or Moises Alou?
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Uniform Distributions
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Normal Distributions
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The Bell Curve
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Normal Curves and Standard Deviation
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Section 8.4Go Figure
Making Inference from Data
If the going gets tough, do something else.
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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?
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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.
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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.
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The Ideas Behind Statistical Inference
Setting 3:Reality contains some probabilistic feature
and we use a random sample to determine what the chances are.
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Confidence Intervals
“Poll shows that Arnold Schwarzenegger will receive 46% of the vote with a margin of error.”
What does that statement mean?
3%
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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 willhave a margin of error of approximately 1
n
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Section 8.5War, Sports, and TigersStatistics Throughout Our Lives
Whenever possible, create an experimentand study the outcomes.
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Question of the Day
Is every possible number equally likely in alottery?
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The Birth of Genetics
Examining data can drawing conclusions from it can have profound consequences.
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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!
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Measuring Relationships
Correlation – the extent to which a relationship exists.
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