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Why Min-Max Normalization Can Produce Values Outside Zero and One

Article Quant Q&A · Author: Jose Maldonado
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Summary

The document addresses a spreadsheet question about min-max normalization, using a last price, a minimum, and a maximum in the standard rescaling formula. The author expects normalized results between zero and one but observes values outside that interval.

The answers identify the likely issue: the minimum and maximum used for scaling do not include the latest value being normalized. If that value is above the chosen maximum or below the chosen minimum, the formula naturally returns a result above one or below zero. Including the current value in the range addresses that specific cause. The post offers no broader discussion of normalization windows, outliers, or whether the latest observation should be included for a particular analysis, so the correction depends on the intended range definition.

Key ideas

  • Min-max scaling maps values to zero through one only when they lie within the selected bounds.
  • A value above the selected maximum can normalize to more than one.
  • A value below the selected minimum can normalize to less than zero.
  • Check that the bounds include the value being normalized when that is the intended range.

Tags

StatisticsTechnical indicators
Full text
# using a normalized formula from a book but not getting the correct values


# using a normalized formula from a book but not getting the correct values












I'm attempting a normalization formula (seen in the picture) but I'm not getting the result of 0 and 1. Instead I'm getting values greater than 1 and less than 0 (seen in the other picture).

I wrote the formula from the picture as =(E3-$V$3)/($W$3-$V$3).

E (last price) V (MIN function of E) W (Max function of E)

any help would be appreciated

## Answer by KaiSqDist (score 0)

https://quant.stackexchange.com/a/79709

I believe that your MAX and MIN values should include the latest values as well. If your MAX and MIN do not include those, then it is possible that $E3 > W3$ or $E3 < V3$, and your normalized value is above 1 and less than 0.

Currently what seems wrong (to me) is that the above step I mentioned is missing.

## Answer by achirikhin (score -1)

https://quant.stackexchange.com/a/79707

Last value should be in the array.

Also in the formula you have "N" and "n", just a typo?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.