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I have a non-normal data set. We need to calculate the average of the numbers in this data set for planning purposes. I used “standardize” to normalize my data in Excel. Can I map the average obtained from the standardized data set back to the original so I have an a new average?


Let me try to clarify some of the questions posed here. The data set has supplies ordered/week. The average of this is going to be used for future planning purposes. Someone suggested that we normalize this data set and then find what the average would be and used the average obtained from normalizing. So my question is if I used the standardize function in Excel and get the new average from the the "standardized" data set can I map it back to my original data set? See example below

"X1" Mean Std Dev Standardized value 
282   252      55               0.52 

Can I find out what 0.52 corresponds to in my original data set? as in would I get something that says 0.52 corresponds to a normalized value of 265 ? If possible i would like to do this for every reading and then find a new average Thank you!

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    $\begingroup$ What are you trying to do? $\endgroup$ – Gala Jul 2 '13 at 20:13
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    $\begingroup$ You sure can: the back-transformed average will equal the average of the original data. :-) (That is because standardization is a linear function.) If you are clever and unscrupulous, you can find ways to "normalize" your data (using standard methods, such as Box-Cox transforms) that will cause the back-transformed average to be literally anywhere between the smallest and largest values in your dataset--take your pick! These considerations bring us back to @Gaël Laurans' comment: what is the purpose of this averaging? How will it be used and interpreted? $\endgroup$ – whuber Jul 2 '13 at 20:18
  • $\begingroup$ Are you trying to figure out how to update averages as new data come in? $\endgroup$ – Glen_b -Reinstate Monica Jul 2 '13 at 23:50
  • $\begingroup$ Let me try to clarify some of the questions posed here. The data set has supplies ordered/week. The average of this is going to be used for future planning purposes. Someone suggested that we normalize this data set and then find what the average would be and used the average obtained from normalizing. So my question is if I used the standardize function in excel and get the new average from the the "standardized" data set can I map it back to my original data set? See example below "X1" Mean Std Dev Standardized value 282 252 55 0.52 Can I find out what 0.52 corresponds to in my original data $\endgroup$ – user27595 Jul 3 '13 at 15:22
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    $\begingroup$ re the edit: Please see my first comment, which demonstrates this particular use of standardization is pointless. $\endgroup$ – whuber Jul 3 '13 at 15:34
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I think you are confusing two senses of "normalize".

Unless otherwise defined, standardization refers to scaling in the sense of (value $-$ mean) / standard deviation. After subtracting the mean and dividing by the standard deviation (SD), the new values necessarily have mean 0 and SD 1. Also, units of measurement wash out.

That could be described as normalizing in senses often met outside statistics, in that different variables once standardized will have the same means and SDs.

But, but, but: if your data are non-normally distributed, meaning not following a normal or Gaussian distribution, that will remain exactly the same after standardization.

All that said, I don't understand your specific question. You should have your data in their original form and in their standardized form. What else do you want?

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