Interpolation and extrapolation, Mathematics

Interpolation is a method of statistical estimation and the word literally means 'making insertions'. Let us consider a well-known situation which requires the use of interpolation. Assume the census is conducted once in ten years. So, typically the exact head count of the population of the country is available only for years 1921, 1931, 1941, 1951, 1961, 1971, 1981 and 1991. If we need to know population of the country for any intermediary year, say, 1985, one logical approach would be to work forwards from the population of 1981, by adding births and inflow of people into the country and deducting deaths and outflow of people from the country during the period 1981 to 1985. Though, this approach would give us an accurate population figure for 1985, the required data on births, deaths, inflow and outflow of people may be difficult to gather and the cost of compiling such data may exceed the benefit that may accrue from the exercise. The population figure for the year 1985, may be required to correlate the demand of a product with the population and the inferences to be drawn may not be highly sensitive to minor variations in the population figure. That is, while the data on population in 1985 is required, a one hundred percent accurate figure is really not required.

This is usually accomplished with a few steps of calculation and the figure so obtained is fairly correct as long as the assumptions underlying interpolation hold good.

Suppose, the same firm by studying the past correlation of demand for its products with the population wants to predict the demand for a future year, say, 1997, through a forecast of the population figure. This is possible through the use of the technique extrapolation.                          

Posted Date: 9/13/2012 8:00:29 AM | Location : United States

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