Standard error of a weighted composite score

I would like to calculate the standard error of a weighted composite score. The composite score is based on the sum of a respondent's rating to a particular question multiplied by a weight (as determined through factor analysis). For this example, please assume that the composite score is made up of 7 questions.

Any help would be much appreciated.


Omega Contributor
I have no idea the best approach given your course. Though, in meta-analyses they provide multiple ways of determining this composite parameter from mulitple contributing manuscripts. May want to check these out if you have no clue of what they want you to do.
Thank you for your message. I wondered if there was a formula that incorporated the variances of each question (7 questions make up the composite score), their respective weights and the correlations between questions? If you know of any formulas I would be most grateful for any further help.