# Questions tagged [geometric-mean]

A measure of central tendency that represents the typical value of a set of numbers when those numbers are thought of as multiplicative in nature.

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### What can one conclude about the data when arithmetic mean is very close to geometric mean?

Is there anything significant about a geometric mean and arithmetic mean that fall very close to one another, say ~0.1%? What conjectures can be made about such a data set? I've been working on ...
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### How can we simulate from a geometric mixture?

If $f_1,\ldots,f_k$ are known densities from which I can simulate, i.e., for which an algorithm is available. and if the product $$\prod_{i=1}^k f_i(x)^{\alpha_i}\qquad \alpha_1,\ldots,\alpha_k>0$$ ...
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### The geometric mean is an unbiased estimator of the mean of which continuous distribution?

Is there any continuous distribution expressible in closed form, whose mean is such that the geometric mean of the samples is an unbiased estimator for that mean? Update: I just realized that my ...
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### Calculate the average rate of population increase per decade of a country

The population of a country increased by 20% in the first decade, 30% in the second decade and 45% in the third decade. What is the average rate of increase per decade in the population? The answer ...
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### Transformation among power-means

It is well-known that arithmetic and geometric mean are strongly related via logarithmic transformation, i.e. if we take arithmetic mean of logarithmic-transformed values we get the same as if we take ...
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### dealing with zeroes while using geometric mean

In case of creating an index using standardised variables(between 0 and 1), how do we deal with the zeroes(while using Geometric mean for aggregation)? it could be the case that only one indicator is ...
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### Is it dangerous to take the mean of ratio measurements?

I'm going through a Computer Architecture course and in one of the lectures they mention that when measuring the difference in runtime performance between two systems, using for example multiple ...
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### Geometric Mean Standard Error [duplicate]

I read from wikipedia that the geometric standard deviation is $$\sigma_g = \text{exp}\left( \sqrt{\frac{\sum_{i=1}^n\left(\frac{A_i}{\mu_g}\right)^2}{n}}\right)\,,$$ where $\mu_g$ is the geometric ...
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### What comes after the geometric mean?

The geometric mean is a multiplicative alternative to the arithmetic mean, which we could call additive mean, thereby calling the geometric mean multiplicative mean. My question is the following: what ...
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### Estimating with the geometric mean

I heard about an interesting technique for making ballpark guesses: If you need a variable that you have no idea about (like the average number of pianos per household), you can try to come up with ...
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### How is that possible that simple arithmetic mean works well even for strongly skewed distribution?

I was taught, that the arithmetic mean is sensitive to outliers and skewness. This was natural to me - the observations lying far from the "central point" of the distribution "pull" the measure ...
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### Arithmetic mean from geometric mean

For the data set the geometric mean is 10 then arithmetic mean will be? I tried hard to calculate the arithmetic mean from geometric mean which is given as 10 but unable to find it.
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### Help with log-transformed data in meta-analysis

I am performing a meta-analysis of pharmacokinetic crossover trials with drug-metabolising enzyme activity as their endpoint(s), and as to be expected, the data are a mess and are reported in a ...
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### Arithmetic mean of normalized scores or a direct geometric mean?

My question is about studies like the following: The 2015 SEDA Scores by Country, PDF is available here. The authors collect 43 indicators for 149 countries and compute a well-being index based on ...
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### What is the geometric mean of the first hitting time distribution of Wiener process?

I'm looking for an analytic formula. Approximate formulas are welcome, in which case I give more importance to simple and nice expressions rather than to precision of the approximation. I'm looking ...
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### Using geometric mean to take median of an even number of data points

When taking the median of a data set consisting of an even number of data points, generally the arithmetic mean of the two middle points is taken. Suppose a set of data points has a suspected ...
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### Is expected value different in meaning from central tendency? Isn't both about “typical values”?

I was taught, that for any distribution having the 1st raw moment defined, the "expected value" is equal to it and it's also the arithmetic mean. "Expected value" sounds to me like "typical value". ...
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### Comparing performance of 2 comparable tests

So I have sets of data, 15 responses for test A and 15 separate responses for test B. Tests A and B have 6 perception questions and the object is to compare the performance of representing data one ...
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### Robinson's Geometric Mean Test

I am reading this book: Ending Spam: Bayesian Content Filtering and the Art of Statistical Language Classification by Jonathan A. Zdziarski page 78 is about the Robinsons Geometric Mean Test. This ...
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### Should I use arithmetic or geometric mean here?

So I have monthly indices (Consumer Price Indices for 12 months) for a given country. I want to calculate the annual average for each country in order to have an average Consumer Price Index for a ...
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### Show that the Geometric Mean $g$ can be expressed as $\log g=a+\dfrac{k}{n}\sum_{i=1}^r f_i(i-1)$

In a frequency distribution the upper boundary of each class interval has a constant ratio to the lower boundary. Show that the Geometric Mean $g$ can be expressed as \log g=a+\dfrac{k}{n}\sum_{i=1}...
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### Geometric mean intuition and interpretation

When simple mean is generally quite an intuitive term, and may be interpreted among others as average value in terms of distance, central value in terms of weight, expected value in terms of ...
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### Geometric mean and geometric standard deviation

When summarizing normalized data (for example, percentage data), one must use the geometric mean instead of the arithmetic mean. Thus, instead of using the arithmetic standard deviation, one shall use ...
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### How would I calculate a combination of the Binomial and Geometric Distributions?

To be specific with my problem, I'm calculating a formula for a game. There's 6 independent trials, each with an independent probability of success = 0.34. I know that from the Geometric distribution, ...
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### Find $E(x^2)$ given $E(log(x))$

Suppose I have a blackbox generating values $x_n$. If I take mean($x_n^2$) it flies all over the place as new values are added -- a supermassive 48-digit value could suddenly ramp up a previously ...
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### Why summarise right-skewed distributed (log-normal) data with geometric mean rather than its expected value?

I am very confused. The first raw moment calculated from sample, the arithmetic mean, is the BLUE estimator of its expected value. So there is no better one. At the same time, I was told that the ...
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### Need advice on acceptable means to convert lower and upper confidence limits of a lognormal distributions to median and geometric standard deviation

I have offered to help convert a monte carlo simulation from guesstimate (a streamlined monte carlo simulation tool) https://www.getguesstimate.com/ to Analytica in order to perform a more in depth ...
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### Geometric mean: Why root instead of divide? [closed]

I use the geometric mean to create standardized ranking between several disparate variables, so I can compare different variables combination: the higher the GM, the higher all the variables will be. ...
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### Compare 2 sets of numbers by Ratio of Geometric means rather than Student t-test

In a medical article published today(!), ratio of geometric means and its confidence interval is used to compare 2 independent groups rather than Student t-test. My specific questions are: What ...
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### Which test should I use to compare three geometric means?

I'm trying to use some test to compare three geometric means of some dataset, to see if there are significant differences. I want to compare A with B, B with C and A with C, but I'm unsure of which ...