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I have some questions regarding the normalisation of a data set between 0-1. The members of the set that I try to normalise are:

X1 = 4.803
X2 = 24.30
X3 = 280.32
X4 = 44.78

If I add them all up I get 354.203. As I want to map each data point to the 0-1 range, I use the following equation:

$$ X_{i,0\;to\;1} = \frac{X_i - X_{min}}{X_{max} - X_{min}} $$

I get:

X1_norm = 0
X2_norm = 0.0707651433486863
X3_norm = 1
X4_norm = 0.14509812461663

I then have two questions: 1) Can I somehow get 354.203 using the normalised values? 2) What should I do in order to map the entire data set to 0-1? That is, if I add all the normalised terms (X1_norm to X4_norm) I want to get exactly 1.

Thanks in advance.

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You have a typo in the formula (should be $-Xmin$ both on top and bottom) and $X_4^{norm} \approx 0.145098125$. – gt6989b Oct 23 '12 at 16:21
Fixed now, thanks – limp Oct 23 '12 at 16:25
up vote 1 down vote accepted

(1) Once you have normalized, your data is in $[0,1]$, so it's not possible to tell what was the original data range, unless you keep original min and max.

(2) Divide all normalized terms by their sum (roughly, $1.215863268$). You get $(0, \ 0.058201564, \ 0.822460902, \ 0.119337534)$

share|cite|improve this answer
Thanks a lot for your answer. One last thing: Let's say that I keep the original min and max. What should I do to retrieve the rest data points (X2 and X4 in my case) by only having the normalised data? – limp Oct 23 '12 at 16:39
@limp Let $x$ be the rescaled point. The original will be $X_\min + x*(X_\max - X_\min)$. If you have rescaled further as in (2), say by another factor $f$, you would need to compute the original value as $X_\min + x*f*(X_\max - X_\min)$ – gt6989b Oct 23 '12 at 16:48
That was really helpful, thanks again. – limp Oct 23 '12 at 16:58

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