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 ?

**Contents**hide

#### Best Answer

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}

### Similar Posts:

- Solved – Why is the sum of the sample autocorrelations of a stationary series equal to -1/2
- Solved – Connection between Hazard Ratios, Survival, and Probability
- Solved – What are some ways to normalize variables to compare standard deviations
- Solved – How to prove that a normalized kernel is also a kernel
- Solved – How to prove that a normalized kernel is also a kernel