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.