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I dont fully understand Zscore, I need to standardise raw data to use them for further uses, so I though about using Zscore. When I calculated it, some of the results I got are greater than 1 and I wonder if I can control these result without ruining the standardisation . Is it possible to calculate zscore and ensure result range between 1 and -1? or i have to use other methods

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The normal distribution has two parameters: the mean and the variance. The z-score is the name of the normal distribution with a mean of zero and a variance of 1. The possible values of this distribution cover the entire set of real numbers. About 68% are within the range (-1, 1). If when you standardized you obtained about 68% of your transformed values between -1 and 1, then that is what you should expect if your distribution is normal.

If your distribution is not normal, and if you are referencing dividing observations by their standard deviation, then the z-score you calculated is a count of how many standard deviations each number is from the mean of your distribution. If a number is more than 1 standard deviation from the mean,then it will have a z-score of greater than 1 or less than -1.

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  • $\begingroup$ It is likely the question refers to the process of standardizing a set of numbers and so has little to do with Normal distributions or their properties. $\endgroup$ – whuber Mar 21 '18 at 22:42
  • $\begingroup$ what i'm trying to do is the standardise raw data and convert them to numbers between 1 and -1 for AI training and yes most of the data between 1 and -1 but I cannot have any data outside this range. is there a way to get all data between this range using SD $\endgroup$ – ma1169 Mar 21 '18 at 22:54
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    $\begingroup$ My answer does not help you. I was confused by your mention of Zscore. $\endgroup$ – Harlan Nelson Mar 21 '18 at 23:12
  • $\begingroup$ How about this. You are able to determine of a number is negative or positive. Take the positive numbers and calculate the empirical cumulative density. Then do the same for the absolute value of the negative numbers, then add the negative sign back in. $\endgroup$ – Harlan Nelson Mar 21 '18 at 23:27
  • $\begingroup$ okay if its called normalisation can i normalise the Zscore value? so after calculating zscore, i do something like .8*(zscore)+.1 to have all the result of specific range. will this mess with the concept of zscore $\endgroup$ – ma1169 Mar 21 '18 at 23:36

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