Skewness and recomputing the average

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In summary, it looks like there is a discrepancy between theory and experiment, which means that the theory might need to be changed.
  • #1
jk22
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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 ?
 
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  • #2
What characteristics would a good measure of average have to you? It all depends on what you want to use this for.
 
  • #3
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.)
 
  • #4
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 ?
 
  • #5
jk22 said:
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.
 
  • #6
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.
 
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  • #7
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.
 
  • #8
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
 

1. What is skewness and why is it important?

Skewness is a measure of the symmetry of a distribution. It tells us how much a dataset deviates from a normal distribution. It is important because it can affect the interpretation of statistical analyses and can help identify outliers in a dataset.

2. How do you calculate skewness?

Skewness is calculated using the formula (3 * (mean - median)) / standard deviation. A positive skewness indicates a right-skewed distribution, while a negative skewness indicates a left-skewed distribution.

3. Is it necessary to recompute the average after identifying skewness?

Yes, it is necessary to recompute the average after identifying skewness because the mean is affected by extreme values in a dataset, while the median is not. Recomputing the average can help provide a more accurate representation of the data.

4. How does skewness affect the interpretation of a dataset?

A high degree of skewness can indicate that the dataset is not normally distributed. This can affect the validity of statistical tests and confidence intervals, as these methods assume a normal distribution. Skewness can also impact the choice of statistical methods and the accuracy of predictive models.

5. What are some techniques for reducing skewness in a dataset?

Some techniques for reducing skewness include transforming the data using logarithms, square roots, or other transformations, removing outliers, or using non-parametric statistical methods. It is important to consider the underlying cause of skewness before choosing a method to address it.

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