Probabilities and their Interpretations

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Probabilities and their Interpretations
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Simple Example

• There are 20 Form 6 students of different
  heights
• Line up the students according to their heights
• Label their respective heights as A, B, C, etc.
• Divide them into 10 groups called deciles (each
  contains one-tenth of the total number)
• Note 100 parts are percentiles ? 1 decile is 10
  percentiles

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• Now suppose the students were sitting randomly in
  a classroom
• If you selected any student, there is a 10
  chance or probability of the student being in any
  particular decile
• You have 30 chance (i.e. 6 out of 20) of
  selecting someone with either height F or lower
  (deciles 1,2,3) or above height N (deciles 8,9,
  10) ? shorter than normal and taller than normal
• There is 40 chance of selecting one of the
  remaining students who have heights greater than
  F and less than equal to N ? near normal.

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Rainfall Probabilities

• A set of rainfall records taken over a number of
  period (at least 30 years)
• Rank all the totals at a location for virtually
  any similar period of whole months
• Divide ranked amounts into ten equal deciles
• Rainfall below the 30th decile (1,2,3) is called
  below normal or below average and above 70th
  decile (8,9,10) is called above normal or above
  average ? climatological probabilities

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TercilesSimple Example

• Roll a fair six-sided die, you chances of rolling
  a 3, are 1 in 6.
• The chances of rolling (unbiased)
• 1 or 2 is two in six i.e. 33
• 3 or 4 is two in six i.e. 33
• 5 or 6 is two in six i.e. 33
• There are three equal groups therefore they are
  called terciles.
• Roll the die many times ? 1/3 of the numbers will
  be in each tercile

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• 2 is the 33rd percentile because 33 of the
  numbers on a die are less than or equal to this
• 4 is the 67th percentile because 67 of the
  numbers on a die are less than or equal to this
• In a bias situation, die is slightly heavier on
  some six faces ? higher chances of occurring

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Rainfall Terciles

• Now for the same set of rainfall values, instead
  of dividing into ten equal parts (deciles),
  divide them into three equal parts (terciles)
• There is equal chance of rainfall falling into
  each tercile (unbiased)
• Tercile 1 ? less than or equal to 33rd
  percentile ? below average ? dry conditions
• Tercile 2 ? between 33rd and 67th percentile ?
  average ? normal conditions
• Tercile 3 ? greater than or equal to 67th
  percentile ? above average ? wet conditions

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• In a bias situation, rainfall is dependent on El
  Niño, La Niña or normal condition
• Examples
• During an El Niño, there is a higher chance of
  below average rainfall (tercile 1) ? 1997/1998
• During a La Niña, there is a higher chance of
  above average rainfall (tercile 3) ? 1999/present