Undergrad Skewness and recomputing the average

[jk22]

Suppose i have a non null skewness. Then this means in some sense that the average computed is not a good measure of average ? How could i recompute an average out of skewness so that it becomes zero and which skewness measure should i take ?

 

[micromass]

What characteristics would a good measure of average have to you? It all depends on what you want to use this for.

 

[FactChecker]

The average is the average, regardless of the skew. More skew means that there will be a larger difference between the mean (average) and the median. That is because one side of the mean has fewer points and they tend to be farther from the mean. (This is a "rule of thumb." There are probably examples where the mean and median are equal but there is a skew.)

 

[jk22]

I mean there are a lot of averages but if the skew is non zero this means there are more results on one side of the previous average hence this average were not a good measure ?

 

[micromass]

I mean there are a lot of averages

Not sure what you mean with that.

but if the skew is non zero this means there are more results on one side of the previous average hence this average were not a good measure ?

Yes, if the distribution in skewed, then there typically will be more observations on one side of the average than on the other side. If you don't want this, then you should use the median.

 

[ssd]

Skewness is one character of the data set, average is another character- measure of central tendency. For moderately skewed distributions 3(mean-median)≈ (mean-mode). You can choose your measure of central tendency which suits your requirement the best. Note that, median will imply equal no. of observations on both sides. Average (well a.m.) and skewness are characterized by 1st and 3rd order moments.
Your presumption is not at all true that "for a skewed distribution a measure of central tendency needs to be corrected." This is because of the fact that measures of CT are developed without consideration of skewness.

 

[FactChecker]

There are 3 common measures of "average".
mean=sum of sample values/number of samples
median=half the sample are greater and half are less
mode=the value that has the most sample points with that value.

The term "average" refers to the mean. Don't say "average" if you are really talking about the median or mode.

You need to be specific about which one you are talking about and use the most appropriate one.

 

[jk22]

Thanks.

To tell more i try to understand why the Bell signal in his nonlocality theorem is experimentally lower than the theoretical prediction : theory <Chsh>=2.82 experiment of hensen 2.40 or ansmann : 2.07

This gives a discrepancy between 20-40% between theory and experiment.

I wondered if quantum theory was so precise if the experimental error does not allow to reach the theoretical value.

My question is in fact linked to the following physics problem : knowing that experimental results taking into account the error does not permit to reach the theoretical value from which point could we say that the theory should be changed meaning that its not an error due to experimental parameters ? It seems to me there is no way to decide this a theorist could always say the experiment is an approximation of the theory