I have a game with levels. I am tracking the time (in seconds) each of my users took to complete a certain level.
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
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