Say I have the following numbers:
10 10 9 5 4 4 4 1
How do i go about calculating the percentile for each score? Is there a standard formula for figuring this out?
Well, if they come sorted like that, you can:
Otherwise, just count how many numbers are <= the number you're looking for, then divide it by the total. The above is just faster for when they come sorted.
The $x$th percentile is the point where $x$ percent of the data lies below. Here you have 8 data points; $1$ is in the bottom $12.5\%$, so it is the 12.5-percentile. $4$ is the (top of the) bottom $50\%$ so it corresponds to the 50 percentile. $5$ is at the top of the bottom $62.5\%$, so it corresponds to the 62.5 percentile. Etc.