If I know values for 0% and 100%, how can I calculate the value at 90%?

Question

If I have 2 values, one representing 0% of a range (lets say 1.0), and another value representing 100% (lets say 20.0), how would I work out what value 90% would be? A formula would be handy if poss. Thanks.

Answer 1

So, I take this to mean you have an interval of values, $[a,b]$ where $a$ is the min and $b$ is the max and you wish to find a point $90\%$ of the way along. We can write $x\in[a,b]$ as $x=a+(b-a)t$ where $t\in[0,1]$. It turns out that the value of $t$ in this formula is the percentage. At $t=0$ we get $a$, at $t=1$ we get $b$, and at $t=0.9$ we get $0.9b+0.1a$.

Again, the general formula (with $t$ as the percentage) is:

$$x(t)=a+(b-a)t=a(1-t)+bt$$

Answer 2

$1=\frac {100}{100}=100$%.

$0=\frac {0}{100}=0$%

$0.9=\frac {90}{100}=90$%

So in your example $90$%$=\frac {9}{10} \cdot (20-1)=17.1$, in a sense that we interpret this as $90$% of interval from $1$ to $20$, which we could write as $[1,20]$, is $17.1$.

In general you get $a$% buy multiplying $\frac {a}{100}$ with the value of which you want to take $a$%.

Answer 3

The interval has a range of $19(=20-1)$.

$90\%$ of $19$ is $0.9\cdot 19= 17.1$

Now you have to add the lower bound: $17.1+1=18.1$

The range from $1$ to $18.1$ represents $90\%$ of the interval $1$ to $20$.

Answer 4

Do you know if response is linear or not? For instance, you could have pairwise (0%,1) and (100%,16) but (50%,8.5) if linear, or (50%,6.25) if based on a quadratic response, or some other value