Terms in a geometric mean equation

In summary, there is no specific terminology for the numbers or terms in a geometric mean equation. The best way to refer to them will depend on the context in which the equation is being used. For example, they could be called the "missing data point" or the "unknown return". In the given conversation, 'a' can be referred to as the "ratio" or the "quotient" of 'c' to 'b', or simply as the "geometric mean multiplier" of 'b' for the geometric mean. Ultimately, the most appropriate terminology will vary depending on the specific situation.
  • #1
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In a geometric mean equation, say 2 x 8 = 16, or a x b = c, what are the words we would use to describe the numbers or terms? Specifically, if you know 'a' and 'c', what do you call 'b'?

For example, in a normal multiplication, a x b = c, 'a' is the multiplicand, 'b' is the multiplier, and 'c' is the product. What do you call the terms in a geometric mean equation? Calling them multiplicand and multiplier seems out of place, as it adds some sort of priority to one of the factors.

If you reverse it, and want to know what one of the missing multipliers is... e.g. what is 'a' if you know 'b' and 'c', so that a= c/b then what do you call 'a'? And what term describes the relation between 'a' and 'b'? A sentence such as:" 'a' is the geometric mean partner of 'b' for the product 'c' (or square of the geometric mean)" is clunky and probably not well stated.

The Wikipedia article, http://en.wikipedia.org/wiki/Geometric_mean, does give terminology. Is there a proper terminology?
 
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  • #2
There is no special term to use. The best way to put it will vary by the context in which the geometric mean is being used.

For instance, if they are samples from a population, and we know all the sample values except one, and we know the geo mean, we would call it the 'missing data point'.

If they are price relatives (aka prels: term in finance for 1 plus the investment earnings in a period) and we know all the prels except one in a time series and we know the accumulation, which is related to the geo mean, we would call it the 'missing prel' or maybe 'unknown return'.

In your example above, you can just call 'a' the 'ratio' of c to b, or the 'quotient' if you prefer'.
 
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  • #3
Thank you andrewkirk.
Maybe " 'a' is the geometric mean multiplier of 'b' for the geometric mean."
This gives priority to the known unit(s), and, in the example of only two terms, let's the reader assume the geometric mean is the square root of the product. That approach keeps the sentence tighter.
 

1. What is a geometric mean equation?

A geometric mean equation is a formula used to calculate the average of a set of numbers that are all multiplied together. It is commonly used in mathematics and statistics to find the central tendency of a data set.

2. How is a geometric mean equation different from an arithmetic mean equation?

The main difference between a geometric mean equation and an arithmetic mean equation is that the arithmetic mean uses addition while the geometric mean uses multiplication. This means that the arithmetic mean is affected by extreme values in the data set, while the geometric mean is not as heavily influenced by outliers.

3. When should a geometric mean equation be used?

A geometric mean equation is most useful when dealing with data that follows a logarithmic pattern or when comparing growth rates. It is also commonly used in finance to calculate rates of return.

4. What are the advantages of using a geometric mean equation?

One advantage of using a geometric mean equation is that it gives equal weight to all values in the data set, making it a more accurate representation of the data. It is also less affected by extreme values, making it a better measure of central tendency in skewed data.

5. What are some real-world applications of a geometric mean equation?

A geometric mean equation can be applied in various fields, such as finance, biology, and physics. In finance, it is used to calculate compound interest and average rates of return. In biology, it is used to measure the growth rate of populations. In physics, it is used to calculate average velocities and accelerations.

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