section 8.1 stumbling through a minefield of data inspiring statistical concepts through pitfalls
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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?. - PowerPoint PPT PresentationTRANSCRIPT
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.
Question of the Day
Would you answer the following questionhonestly in public:
Have you been drunk in the past 48 hours?
Graphically distorted data
Graphically distorted data
Collecting Data
Leading and misleading dataSurveys can produce skewed results by phrasing the questions in ways that might bias the answers.
Collecting Data
Sample Bias – Polluted PoolsThe 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 8.2Getting Your Data to Shape Up
Organizing, Describing, and Summarizing Data
Search for the most effectivemeans 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 DataStem 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 ValueFirst QuartileSecond Quartile (Median)Third QuartileMaximum 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 8.3Looking 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 8.4Go 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 margin of error.”
What does that statement mean?
3%
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
Section 8.5War, Sports, and TigersStatistics Throughout Our Lives
Whenever possible, create an experimentand study the outcomes.
Question of the Day
Is every possible number equally likely in alottery?
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.