I have only summary statistics for each state in the United States. I have the mean and median prices for each state and that’s it.
How can I estimate an “overall” median price for the nation? I understand whatever I calculate won’t be a “true” median due to the lack of raw data, but I still need a number.
Can I somehow estimate percentiles with this information and find the 50th percentile? A weighted “average” is not that reliable I feel So I would really appreciate some guidance.
*Edit: I am currently using a weighted median and I would like to improve upon that and make it more complex/exact to avoid large differences in prices.