What I want to accomplish is to show the user how their time compares to others (i.e. "Your time is better than 60.5%") by using the existing data that I have.

From the raw data, I've extracted a sample of 1000 that represent each 1000th quantile. Based off of this, I was able to determine the basic properties of the distribution.

Mean 90,47152847

Standard Error 1,951841119

Median 75

Mode 300

Standard Deviation 61,75348928

Sample Variance 3813,493439

Kurtosis 2,127713313

Skewness 1,449926474

Range 296

Minimum 4

Maximum 300

Sum 90562

Count 1001

Is there a way to determine what quartile a certain user time would represent, just by using the above descriptive statistics, and not using the quantiles that I already have?

Reason why I would like to avoid comparing user time to a huge table of 1000 numbers is to save space in the code. So I am hoping for some way to calculate what quantile a user is near/at by using least amout of numbers