Descriptive Statistics

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Descriptive Statistics

• Dr. David Cornforth
• School of Information Technology and Electrical
  Engineering
• University of New South Wales _at_ ADFA

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Types of data

• Qualitative
• Do you like watching movies?
• What is your favourite colour?
• Quantitative
• E.g. How many times a month do you visit the
  cinema?
• What are the red, green and blue components of
  this colour?
• We are talking about the second type

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Qualitative data

• Binary patient allergic to pollen? TRUE / FALSE
• Categorical Colour red, blue, green
• Character letters in a book, sequence of DNA
• Relational animal A is paired with B, site of
  infection is below the eye
• Sets names of a person's children
• Rules "IF spring THEN birds build their nests"
• Pictorial photographs or diagrams.
• Maps spatial arrangements
• Descriptive/Anecdotal notes, comments,
  impressions etc.

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Types of Variables

• Nominal / categorical
• Labels are assigned to things e.g. colour
• Cannot do any maths
• Ordinal
• Items are ranked e.g. race position,
  big/medium/small
• Can compare
• Interval
• Same interval between numbers e.g. temp in degree
  C
• Can compare, add, but not divide
• Ratio
• Values have a real zero point e.g. temp in Kelvin

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Central tendency

• Arithmetic mean - sum of all measurements divided
  by number of observations
• Median - the middle value
• Mode - most frequent value
• Geometric mean - nth root of product of n values
• Harmonic mean - reciprocal of mean of the
  reciprocals of values

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More Central tendency

• Quadratic mean or root mean square (RMS) - square
  root of mean of squares of values
• Generalized mean - nth root of mean of the nth
  powers of values
• Weighted mean - values multiplied by weights
• Truncated mean - mean after discarding highest
  and lowest
• Interquartile mean - a special case of truncated
  mean
• Midrange - mean of the highest and lowest

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Measures of dispersion

• Variance
• Standard deviation square root of variance
• Range max value - min value
• Inter-quartile range like range, but use only
  middle 50 of data

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Useful links

• See Demonstration.xls, sheet Norm.Dist
• http//www.anu.edu.au/nceph/surfstat/surfstat-home
  /1-2-3.html