I have one two data sets of scalar values: one large data set (about 700 data points) and one small data set (80 data points). I would like to update the large data set with the small one using the Bayes’ theorem, and so create another large data set (posterior).

The large data set serves as prior, and it is assumed to be normally distributed and so the posterior. This was motivated by the existence of the closed-form expression of the posterior distribution parameters https://en.wikipedia.org/wiki/Conjugate_prior (the first row in the table for Continuous distributions) for the conjugate prior.

However, if I substitute into the closed-form expressions for posterior mean and variance, using the mean and variance values of prior (inferred from the large data set) and local data (inferred from the small data), the resulting posterior distribution does not make sense.

Do I misunderstand that I can simply substitute into these closed-form expressions the known values in order to get the posterior distribution?