2 7 exploratory data analysis
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2 7 exploratory data analysis

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2 7 exploratory data analysis 2 7 exploratory data analysis Presentation Transcript

  • 5-number summary
    • Minimum,
    • Lower quartile,
      • Quartiles are relatively insensitive to unusual values
    • Median (second quartile),
    • Upper quartile, and
      • Interquartile range = Q 3 – Q 1
    • Maximum.
  • For example
    • 25 55 59 59 63 71 71 74 80 80 80 83 84 84 87 88 95 95 100 100
    • Minimum
    • Lower Quartile (Q1)
    • Median
    • Upper Quartile (Q3)
    • Maximum
  • Boxplot (box and whiskers diagram)
    • Depicts the 5-number summary
    • Useful for comparing to data sets.
  • Components
    • Number line extends from the theoretical (or practical) minimum value to the theoretical (or practical) maximum
    • A box spans the lower and upper quartiles
    • Dotted line through the box at the median
    • Whiskers extend from the box to the minimum and maximum
  • Outliers
    • Outliers are:
      • Less than the lower quartile minus the 1.5 times the inter-quartile range, or
      • Greater than upper quartile plus 1.5 times the interquartile range
  • Live Example
    • Minimum
    • First Quartile (Q1)
    • Median
    • Third Quartile (Q3)
    • Maximum
  • Your turn
    • Use a box and whiskers diagram to compare the 2005 and 2008 September temperatures
      • Daily high temperatures for Trenton
    • Identify any outliers
    • 79 79 83 82 83 85 91 86 85 75 73 77 76 68 66 70 73 78 83 84 81 90 82 89 90 86 78 75 75
    • 86 90 88 92 90 77 81 81 73 74 74 68 83 91 81 68 75 75 68 70 81 73 72 74 66 65 71 69 70 71
  • Two Ways to Characterize Data x i < X – 2s x i > X + 2x x i < Q1 – 1.5  IQR x i > Q3 + 1.5  IQR Outliers Distribution spread, frequency diagram, bar chart and Box and whiskers diagram Picture X and s Minimum, first quartile, median, third quartile, maximum Statistics Mean and standard deviation 5-number summary