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Probabilities and their Interpretations

This article explores the concepts of probabilities in the context of heights and rainfall. Through simple examples, we illustrate how to classify data into deciles and terciles for better understanding of distributions. We demonstrate how to align students by height and divide them into groups, calculating the probabilities of selecting individuals from various categories. Additionally, we analyze historical rainfall data, emphasizing differences in rainfall classifications and climatic influences such as El Niño and La Niña.

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Probabilities and their Interpretations

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    1. Probabilities and their Interpretations

    2. 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

    3. 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.

    4. 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

    5. 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

    6. 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

    7. 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

    8. In a bias situation, rainfall is dependent on El Nio, La Nia or normal condition Examples: During an El Nio, there is a higher chance of below average rainfall (tercile 1) ? 1997/1998; During a La Nia, there is a higher chance of above average rainfall (tercile 3) ? 1999/present

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