I don't think the calculation says anything about the grouping of data. Or does it?
If you have an unbiased sample of 584 votes and 60% of the sample responded "25 - 30", could you say with 95% confidence that 60% (+/-4%) of the sampled population would select "25 - 30"?
I'd imagine there's a lot of science to polling which this calculation probably ignores.
Yep, everything about being sure we have an unbiased sample, which is not likely for a question like this.
What does your calculation say about the grouping of the data into categories?