How to estimate population statistics for each category?

I have data from a simple random sample having n elements which I’m using to estimate my population statistics (mean). My population can be divided into k categories, and I know the composition of my overall population in terms of these categories. As part of my study, I want to estimate the statistic for each category of my population. Unfortunately, I do not have a stratified random sample with me.

Question - Given what I have, is there any way to fairly estimate my population statistic for each category of my population ?