Descriptive Statistics

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Descriptive Statistics

• 01/24/2006

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Review

• Probability Theories
• Normal Distribution Statistical Models
• Calculate normal probabilities
• Central limit theorem
• Other distributions in Normal family

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What do we observe in reality?

• Hedge Funds Investment Example
• If we invest x in mutual fund I, its worth
  after 1 year is distributed X_I N(1.05 x,
  0.0002 x2)
• Weight (Y) distribution of students in 2028B
• Y N(160, 100)

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Relationship of Data and Model

• Shoes
• Foot
• Fit

• Models Normal, Binomial, t
• Data (x1, x2, )
• Fit

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Descriptive Statistics

• Part I. ? X is a random variable (w/probability
  distribution.)
• We assume knowledge about X
• distribution (parameters)
• mean, variance, etc
• Part II. ? Study of sample data (X1, ,Xn)
• We dont know all the parameters
• if we did, why get data?
• use data to estimate the unknown parameters
• use data to make decisions about parameters
• Connection Assume data (X1, ,Xn) are
  realizations of a random variable. We
  characterize its distribution by estimating
  parameters

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Probability distribution f(x)
Experimentation
Probability theory
Data set x1, x2, xn
Data analysis
Statistical Inference
Estimate properties of f(x)
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Data exploration and presentation

• Categorical data (Nominal data)
• Numerical data
• --integers
• --real numbers
• Charts
• Collect observations into groups to construct
  frequency histogram. Often, this is the BEST way
  to communicate your findings from a set of data
  (People understand histograms)

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Categorical data
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Bar Chart
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Misleading Bar Chart
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Pie Chart
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Histogram

• We can (generally) rely on computers to generate
  histograms
• Keep bin widths equal
• Choose width that summarizes the data best
• Use Excel, Minitab, SAS, etc

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Histogram of scores in Quiz 1
Descriptive Statistics Mean 8.120 Standard
Deviation 1.740
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Conveying Information Graphically
Time Series
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• Quiz 2 this Thursday
• Homework 1 is due on this Thursday