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Say there is a skewed data set with a average of 35 and max and min points are 55 and 12 respectively. I want to know whether it is possible to transform this data set to a normal distribution so that the mean of the transformed data becomes 55? Hope the question is clear. Thanks

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    $\begingroup$ It's impossible to tell with the information provided. Why do you want to do that? It seems rather a strange thing to want to do. $\endgroup$ – Glen_b Sep 24 '15 at 3:55
  • $\begingroup$ @Glen_b I just want to know whether something like this is possible. It's for a set of marks. most have got below 50 and therefore a statistically justified addition of marks I believe is the best way to go about to pass some of them $\endgroup$ – Donald Edwards Sep 24 '15 at 4:17
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    $\begingroup$ The issue is basically that if you have many tied values, no amount of transformation will separate them; if not, some transformation is likely to be possible, but there's no guarantee it will seem to make sense. [I think "statistically justified" in this context is pretty meaningless.] Linear rescaling is easily accomplished which will give you some of what you want (and piecewise linear might give you more of what you want), but why do you need normality? $\endgroup$ – Glen_b Sep 24 '15 at 5:32
  • $\begingroup$ @Glen_b thanks for the answer. To get someone at 35 to 50 I have to find a way to increase by 15 but then again I do not want to make 55 go up to as high as 70! So I guess what I want is to change the two end points at a much lower magnitude than those within the range $\endgroup$ – Donald Edwards Sep 24 '15 at 5:52
  • $\begingroup$ If you can figure out what you want 12, 15, 20, 25, 30, ..., 55 to map to, you will have largely solved your problem (linear interpolation in between should be fine, I would think). I'd start with the endpoints and the middle, and then work on something in between those, and then in between those. However, you probably won't get it more than very roughly the shape you want. $\endgroup$ – Glen_b Sep 24 '15 at 6:22
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Box-Cox normality plots will help you decide if there exists a transformation that make the transformed data normal.

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