How to normalize multiple values

Question

I have three values, two of them are from $0 - 144$ and one is from $0 - 24$. I want to normalize these values and end up with a value from $0 - 1$ or $0 - 100$. I wanted to know if I can use the following equation to do this? And if so, how to go about it.

$$ z_i=\frac{x_i-\min(x)}{\max(x)-\min(x)} $$

where $x=(x_1,...,x_n)$ and $z_i$ is now your $i^{th}$ normalized data.

Applying this to my example, if I have three values to get an overall number from $0-1$ or $0-100$ do I have to do put each value individually though this equation and then add them or can I add the values together and use this as the max and do it this way? Also for min wouldn't this always be zero ?

Answer 1

If you want to scale your values with range $[\min,\max]$ to the new range $[a, b]$ the formula is:

$$ z_{i} = \frac{(b - a)(x_{i} - \min(x))}{\max(x) - \min(x)} + a $$

Apply this formula for each of your original values. Here is an example: Say you have three values $x_1, x_2, x_3$. The first two values have a range of $[0, 144]$ and the third has a range of $[0, 24]$. You want to transform all three to have a new range of $[0, 100]$. Let's say your values are: $x_1 = 133.43, x_2 = 51.65, x_3 = 6.91$. The corresponding transformations are thus:

\begin{align} z_1 &= \frac{(100 - 0)(133.43 - 0)}{144 - 0} + 0 = 92.66 \\ z_2 &= \frac{(100 - 0)(51.65 - 0)}{144 - 0} + 0 = 35.87 \\ z_3 &= \frac{(100 - 0)(6.91 - 0)}{24 - 0} + 0 = 28.79 \\ \end{align}