I am currently working with monthly data and I try to calculate confidence intervals for the monthly average. I have data from from 2010 to 2019 and there seems to be some seasonality.

The statement I want to make, is: In december 2020, we expect a value of x which lies with a certainty of 95% between y and z.

For the expected value x, I use the average december values of 2010 to 2019.

For the confidence interval, I am not sure:

My initial guess was to use all months (Jan-Dec) to calculate the standard deviation for the entire dataset to get the confidence intervals (assuming normal distribution of the data). -> One standard deviation for the entire data set.

However, on second thought, I was wondering whether I should use only the data for the month of December to estimate the confidence interval of that month.-> 12 standard deviations, one for each month.

Can somebody help me to figure out which approach is correct?

Thank you very much for your help!