11) The past several years in Florida have seen less than normal rainfall. This

Question

11) The past several years in Florida have seen less than normal rainfall. This past summer we saw above average rainfall. Two different weather forecasters commented: "Since we had so many dry years we were due the heavy rains this past summer" a second one said "I predict rainfall to be above average for the next several summers to get us back to our average". Explain (in statistical terms) what the weather people are saying and if we should believe them, also if any assumptions are being made.

Explanation / Answer

The first forecast says that because there have been less than normal rainfall in Florida in past several years, the upcoming rain is expected to be heavy so that the overall average normal level of the rain in a year in Florida is maintained at its usual value. This forecast is alluding to the Law of averages which says that "Future events are likely to turn out so that they balance any past deviations from the presumed average".

The second forecast says that due to the fact that for past several years, there have been less than normal rainfall in Florida, the upcoming few years will experience above average rainfall so that it compensates for the low rainfall in past years in order to maintain a presumed average value. This forecast is also based on law of averages.

The assumption being made in both the forecasts is that the Actual probability distribution of the annual rainfall does not change as time passes. Only when we make this assumption, we can apply law of averages. Therefore, we can believe both the forecasts only upto the extent that the underlying true distribution of the annual rainfall is stationary over time.

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