# Converting 1 Distribution to Another

#### zeloc

##### New Member
I have a set of values ranging from .01 to 918 with n = 7368. About 3000 values are below 1 and about 150 values are greater than 100. The mean and standard deviation are 9.85 and 47.91.

I would like to convert these numbers to a ranking so that the lowest one is assigned the number 1 and the highest 7368. Unfortunately I cannot just sort them and I need an equation that would take a number in the first group and give the number in the second group.

I have tried converting the initial raw scores into z scores and then converting them to a new scale with a mean of 3684 and SD of 2126.81 (which would be the mean and SD of a set of numbers going from 1 to 7368) but the results are nothing close to the linear relationship I want. The numbers start around 3200 and go up to 44,000.

Does anyone know how I can do something like this, even if it is not perfect? More generally, how I convert other distributions into a ranking using mathematical formulas? I am willing to read and study what I need to if someone can point me in the right direction.

Thanks!

#### Dragan

##### Super Moderator
I would like to convert these numbers to a ranking so that the lowest one is assigned the number 1 and the highest 7368. ... More generally, how I convert other distributions into a ranking using mathematical formulas? I am willing to read and study what I need to if someone can point me in the right direction.

Thanks!
Here's an algorithm that will rank data. You will first have to sort the data.

N=SAMPLE SIZE
INPUT: XO=ORIGINAL DATA; XS=SORTED DATA.
OUTPUT: IRX=RANKED DATA

DO 5 I=1,N
DO 10 I2=1,N
IF (XO(I) .EQ. XS(I2)) GOTO 8
10 CONTINUE
8 IRX(I)=I2
5 CONTINUE
END

#### zeloc

##### New Member
Thanks for the post.

In the application I am running I am not able to enter any programs, I can only enter a mathematical formula that would take 1 value and display another. That looks like a computer program, do you know if there is any way to do this mathematically even if it means using 2 or 3 separate equations to convert each portion of the initial set to the distribution I am looking for?

#### zeloc

##### New Member
Have done some more thinking on this, the easiest way might be to divide all numbers by 918 and then multiply every number by 7000. This wouldn't give me a ranking, but would produce values between 1 and 7000 which I would then do for each set and have a way to compare these numbers to each other. Is there any way to get closer than this approximation?

#### Outlier

##### TS Contributor
I have a set of values ranging from .01 to 918 with n = 7368.

I would like to convert these numbers to a ranking so that the lowest one is assigned the number 1 and the highest 7368.
Unless I'm missing something, I used the Excel functions SLOPE and INTERCEPT to solve the equation for this straight line, which is of the form Y = aX +b, where a is the slope and b is the Y intercept.

Y, which ranges from 1 to 7368, is 8.025141886 [= a] times X, which ranges from 0.01 to 918, plus 0.919748581 [= b].

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#### zeloc

##### New Member
This is exactly what I was trying to do, thanks!