Calculating a percentage of an abnormal distribution

Hello!

I need a formula(s) which will allow me to plug in a number and yield a percentage based on an abnormal distribution of data. For example, given this data set:


16=0%
18=5%
20=25%
23=50%
27=75%
33=95%
38=100%


If I were to plug in 24, the correct answer should be ~55%. I've tried percentage commands, but since this is a skewed data set they won't work because they work on a normal distribution.

Some additional info: The Mean of this data set is 24.2 with a standard deviation of 4.7, Sk=0.6 and Ku=-0.2

Please help and if any additional information is needed I will be happy to provide it. Thanks in advance.

A little more about what I am try to do:
I'm trying to write a test scoring program where raw scores are converted to percentages, and then subsequently standard scores (not worried about the standard score part yet). As opposed to having a data array showing what raw scores align with which percentiles, I have a list which shows me the means, standard deviations, etc as well as different points for distribution percentages. (i.e. 0%, 5%, 25% etc.). I would image these numbers are based on some sort of linear function but I have no way of predicting scores between each percentile interval. Ultimately, I want excel to basically take the number (in this instance 24), find it along this array, and then report the percentage based on the range of numbers (55%).

Originally Posted by protonLeah

Here's a simple linear example:

y =Y_1+(_X-X_1)*(Y_2-Y_1)/(X_2-X_1)

Okay this works great! But now I need about 61 of these and I don't know how to set this up. The calculated Y% isn't able to copy and paste.

Nevermind, figured it out. Thanks!

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use this in cell B1 that will predict percentage on basis of cell A1.

interpolation