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It seems that the popular solution to dealing with skewed data is to apply log-transformation.

But in my case, the data is a rating score (range form 0-5). The distribution of the data looks like exponential distribution where there is really high number of 0 but very few 5.

data distribution

I tried log-transformation but it doesn't work at all. As I understand, log-transformation works only when the data have a wider range (like 0-1000) which it will follow Benford's law.

How could I transform it into normal distribution? or any suggestion to reduce this skewness?

More info:

  1. My aim is not to focus on this particular task but ask for the more general idea where log-transformation cannot apply to resolve skewness.

  2. the example above is discrete on range 0-5 with increments the value by 0.5 on each step.

Imtk
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    Why do you want to transform your data? What are you doing with your data? Also, it looks like your ratings are not discrete between 0 and 5, so what are they actually? – Stephan Kolassa Jan 28 '21 at 08:19
  • What do you really want to do with your data? Regression? If so, look into *ordinal regression*, search this site. – kjetil b halvorsen Jan 28 '21 at 13:26
  • Data is discrete with width = 0.5. I would like to do regression but actually, I would like to get an idea to work with this kind of data as it cannot apply log-transformation in this case. – Imtk Jan 28 '21 at 13:52
  • You don't need transformations. Look at **ordinal regression** https://stats.stackexchange.com/questions/410421/analysis-for-ordinal-categorical-outcome and search this site! – kjetil b halvorsen Jan 29 '21 at 02:14
  • It seems that you answered the wrong question – Imtk Jan 29 '21 at 13:40

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