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index number using geometric mean


Sometimes the arithmetic mean will be useful, but don’t use it just because it’s familiar. Extreme One archetype of skewed data is the “lognormal” distribution. The arithmetic mean will not make sense in this case either.The geometric mean can be useful in many other situations. The perils of this can be seen in the example: 44% of the elements are 9s, but that value does not affect the median: the 9s could be anything, even 1 million each, and the median would remain 2.You would usually just call this the “mean” or, if you’re sloppy with words, the “average” (like Microsoft Excel does): add everything up and divide by the number of elements. The results will also not be the same as in the first procedure either, as you can see.Finally, I’ve also seen some people add the smallest value in their dataset to every value. Geometric mean index numbers are a multiplicative aggregation of (price or quantity) ratios with their importance exponents/weights derived from one or more observed budget shares. The reason is, the geometric mean is indifferent to the scales used (as long as the same ones are used each time).For instance, you can combine a 570 SAT score with a 5/6 entrance essay, and 3 stars for sports, and 95% likelihood of paying tuition — you don’t have to try normalizing the scores first. In our example this is 2:Medians are useful for dividing the data into two halves, each with the same number of elements — e.g. Which investment should the investor choose?The investor will use the future value or the present value formula, which is derived from the geometric mean. But don’t do this simply out of convenience: the results have to be meaningful.Second, if zeros can reasonably be interpreted as non-responses, which shouldn’t really count at all, they can be deleted. For example, replacing 30 with 100 would yield an arithmetic mean of 25.80, but a geometric mean of just 9.17, which is very desirable in certain situations. When a data set contains a large number of repeated values, you can simplify the process of computing the mean by using weights — the frequencies of a value in a sample or a population. If we replace the percentages with their geometric mean, the kitty grows to the same final value, $588.Textbook problems are likely to call for a geometric mean. The geometric mean is 1.0256 which equals 2.56% average growth per year.The geometric mean won’t be meaningful if zeros are present in the data. The key is to recognize when a measured variables is affected by many (semi) independent forces, each of which scales that variable up or down — rather than simply adding or subtracting a fixed amount to it.

You may be tempted to adjust them in some way so that the calculation can be done. You can then compute the geometric mean as a weighted average.

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index number using geometric mean