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Good to see so many responses to a statistical question. Why can we not use CLT to convert all Non-Normal data to Normal? There are different perspectives with which this question has been answered. Sample data may be expected to show normality and may actually show non-normality because of incorrect sampling method (or incorrect grouping, closeness to zero or poor resolution of instrument etc.) and we may like to change our approach. Many times, looking at data in its true individual form is essential and we do not want to miss the underlying reasons for Non-normality. Sample data may have outliers that have unusual reasons which sometimes need to be segregated. Again, we may not like to lose the originality by just taking averages. This is why R charts are seen before X bar charts mostly. Sample data may have come from a population that is truly non-normal. It may either follow another distribution or we may like to not assume a specific distribution. In all the above cases, if we wish to deal with individual values and therefore predict individual outcomes, we may go to the extent of transforming data or even using non-parametric methods. CLT in all such cases is of no use to us. As an example, if I want to deal with the height range of individuals and not the range for average heights of groups, I will not use CLT. If I am focusing on detonation time of hand grenades, it is easier to understand that sample averages will be of limited interest. So, the crux of the issue is that CLT is not useful (in terms of converting non-normal data to normal) when we want to deal with individual data and not sample averages. This point was brought forward by Atul directly and his answer is selected as the best.