# standard error when looking at means of means

I understand reporting standard error when looking at means of a variable say $X$. I am computing this mean across many categories $X_i$, where the mean for a single category is $\mu(X_i)$.

However, when I am looking at means of means which is $\mu_{grand}(\mu(X_i))$ what is a meaningful error if there is no equal variance across categories?

Adding context to explain unequal variance:

If for example the different categories are different drug (opioids) use which has high variability and I am looking at the mean addiction rates across all opioids, how would I describe a standard error?

• what is a meaningful error if there is no equal variance across categories ? please elaborate ? Give something about the context as well. – Subhash C. Davar Jan 27 '18 at 3:13
• @subhashc.davar I added some context in an example which explains what I am trying to answer. – knk Jan 27 '18 at 3:46
• Please state your objectives/ and hypotheses ? what is "meaningful error"? why do you want to compute mean of means ? – Subhash C. Davar Jan 27 '18 at 3:58
• I am looking at a difference in these means - I want to say something about the grand mean across different countries or states – knk Jan 28 '18 at 5:07