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    <p>Let's say you want to scale a range <code>[min,max]</code> to <code>[a,b]</code>. You're looking for a (continuous) function that satisfies</p> <pre><code>f(min) = a f(max) = b </code></pre> <p>In your case, <code>a</code> would be 1 and <code>b</code> would be 30, but let's start with something simpler and try to map <code>[min,max]</code> into the range <code>[0,1]</code>.</p> <p>Putting <code>min</code> into a function and getting out 0 could be accomplished with</p> <pre><code>f(x) = x - min ===&gt; f(min) = min - min = 0 </code></pre> <p>So that's almost what we want. But putting in <code>max</code> would give us <code>max - min</code> when we actually want 1. So we'll have to scale it:</p> <pre><code> x - min max - min f(x) = --------- ===&gt; f(min) = 0; f(max) = --------- = 1 max - min max - min </code></pre> <p>which is what we want. So we need to do a translation and a scaling. Now if instead we want to get arbitrary values of <code>a</code> and <code>b</code>, we need something a little more complicated:</p> <pre><code> (b-a)(x - min) f(x) = -------------- + a max - min </code></pre> <p>You can verify that putting in <code>min</code> for <code>x</code> now gives <code>a</code>, and putting in <code>max</code> gives <code>b</code>.</p> <p>You might also notice that <code>(b-a)/(max-min)</code> is a scaling factor between the size of the new range and the size of the original range. So really we are first translating <code>x</code> by <code>-min</code>, scaling it to the correct factor, and then translating it back up to the new minimum value of <code>a</code>.</p> <p>Hope this helps.</p>
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    1. POHow to scale down a range of numbers with a known min and max value
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    1. USirritate
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    1. COI appreciate your help. I figured out a solution that does the job of looking aesthetically pleasing. However I will apply your logic to give a more accurate model. Thanks again :)
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    2. COJust a reminder: The model will be more accurate with `max != min` otherwise the function results indetermined :)
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    3. COdoes this ensure that my rescaled variable retains the original distribution?
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