Propagate Standard Deviations across multiple averages

Hello, I have a set of data for which I'm trying to propagate std deviations across multiple averages. Here's is kind of a simplified example of what I'm trying to do. I have 3 flavors of ice cream (chocolate, vanilla, strawberry). For each flavor I have multiple variables Stratified over time. Eg: Chocolate: Number of adults ordered, # kids ordered, #infants ordered. Then split by months (Jan, Feb, Mar)... Same thing for vanilla, strawberry.

I've done an average across all of time for each flavor - to get Chocolate: avg number of adults ordering over all 12 months (avg1, std1) Avg number of kids ordering over all 12 months (avg2, std2) Avg number of infants ordering over all 12 months(avg3, std3) Same for van, strawberry.

I am then trying to simplify it to one number with a standard deviation where I now average number adults, kids, infants. This will again have an average and standard deveiation (avg4,std4) across all people and all 12 months. But I don't know how the standard deviation of the initial 3 averages will affect the final standard deviation?

In the end I hope to have a bar graph with chocolate, vanilla, strawberry on the X axis, the Y will be their averages across all people and all 12 months, with error bars showing the std deviation