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Spread: Home on the Range

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Presentation Transcript
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Chapter 5 : Describing Distributions Numerically I. Finding the Center: The Medianmidrange_ - (highest + lowest) / 2 sensitive to outlying valuesmedian the middle value that divides the histogram into 2 equal areas (include units)After you find it ask yourself how well it actually summaries the dataIf odd number of values ; if n is even there is 2 middles so Find the median of the values:12, 15, 38, 25, 12, 15, 16, 22, 13, 33, 11, 25, 16, 18, 23, 18, 19, 13, 14 Median: _______12, 15, 38, 25, 12, 15, 16, 22, 13, 33, 11, 25, 16, 18, 23, 18, 19, 13, 14, 16 Median: _______
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Spread: Home on the Range
  • The more the data vary, the less the median alone can tell us. So, you should always report a measure of spread.
  • Range: max – min (single number, not an interval, also sensitive to outliers)
  • Spread: The Interquartile Range
  • Concentrate on the middle . (ignore extremes)
  • Quartiles – divides data into 4 equal parts

Lower Quartile (Q1) Median (Q2) Upper Quartile (Q3)

  • Interquartile Range(IQR): Upper Quartile – Lower Quartile
    • Textbook includes median in each half, graphing calculator does not)
  • Lower Quartile 25th percentile); Upper Quartile (75thpercentile)
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5 Number Summary
  • Reports a distributions median, quartiles, and extremes (min, Q1, median, Q3, max)
  • Making Boxplots
  • Box plot– displays the 5 number summary as a central box with whiskers that extend to the non-outlying data values
  • Particularly effective for comparing distributions.
  • Fences - used to identify outliers
  • (help with construction, but never include in your boxplot)
    • If a data value falls outside one of the fences, we do not connect it with whiskers
    • Lower Fence: Q1 – 1.5IQR
    • Upper Fence: Q3+ 1.5IQR
slide5
Mean or Median?
  • Mean cuts the data into 2 halves not taking into account their size
  • Median takes their size into account (the point at which the histogram would balance)
    • Left Skewed → mean to the left of the median
    • Right Skewed → mean to the right of the median
  • If data is skewed better to use themedian_.
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What about the Spread? The Standard Deviation
  • IQR is good but ignores individual data
  • Standard deviation– takes into account how far each value is from the mean
    • Only appropriate for symmetric data
    • Deviation– distance a value is from the mean
    • Could average them but the + and – would cancel each other out, so we square them
    • Standard Deviation_ – the average (almost) of the deviations
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Shape, Center, and Spread
  • So…
  • Skewed →IQR & MEDIAN
  • Symmetric → MEAN & STANDARD DEVIATION
  • Outliers → median / IQR_ OR Mean / standard deviation without outliers
  • Read page 87 (What Can Go Wrong) and 88- 89 (Terms)
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