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I have a collection of numbers between 19.75 and 20.25 and a number that is between that borders lets say its 20.10.

Now basing on that need to calculate equivalent of that number (20.10) but in collection between 120 and 160.

I think what I am trying to say what would be equivalent of a number from first collection in a second (number between 120 - 160)

Wojciech Szabowicz
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  • This is not clear. What, if anything, is the connection between your "collection of numbers" and the single specified number? – lulu Jan 31 '19 at 10:58
  • How do you define the "equivalent number"? Is it so that if you scale the numbers with some constant, the resulting numbers are equivalent? – Matti P. Jan 31 '19 at 10:59
  • I'm just guessing but you could use a transformation that (in the first example) makes $19.075 \rightarrow 0 $ and $20.25 \rightarrow 1$. If the function is linear, then $20.10$ is transformed into $$ \frac{20.10 - 19.057}{20.25 - 19.075} \approx 0.872 $$ is this somewhere near what you mean? So that just means that $20.10$ is $87.2~%$ of the way between $19.075$ and $20.25$. – Matti P. Jan 31 '19 at 11:02
  • Aye @MattiP. that is exactly what i mean, Now that i now that percantage, how to get info what that value is in other collection? – Wojciech Szabowicz Jan 31 '19 at 11:21

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The idea here is to consider a set with a known minimim and maxmim values. We want to make a transformation that associates a number between $0$ and $1$ to every element in the set, so that the minimim value gets transformed into $0$ and maximum value gets transformed into $1$. All the other values are then somewhere in between. For any set, this transformation is $$ f(x) = \frac{x - \text{min}}{\text{max} - \text{min}} $$ It's easy to see that $f(\text{min}) = 0$ and $f(\text{max}) = 1$.

In the example case, we have $\text{min}= 19.75$ and $\text{max}= 20.25$. We want to transform $x=20.10$, resulting in $$ f(20.10) = \frac{20.10 - 19.75}{20.25 - 19.75} = 0.7 $$ The question was, which value gets transformed into this value ($0.7$) when $\text{min}=120$ and $\text{max}=160$. We just need to form the equation: $$ \frac{x - 120}{160-120} = 0.7 \qquad \Rightarrow \qquad x - 120 = 28 $$ and therefore $x=148$. We can check the result: $$ \frac{148 - 120}{160-120} = 0.7 $$ Therefore, the answer of $x=148$ is correct.

Matti P.
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