For histogram-like functionality, you can compute factor sets, i.e., subsets that have identical values for one or more columns, and you can compute aggregate functions for them.
SELECT COUNT(*) AS n, ROUND(phot_g_mean_mag) AS bin, AVG(parallax) AS parallax_mean FROM gaiadr1.tgas_source GROUP BY bin ORDER BY bin
Note how the aggregate functions interact with grouping (they compute values for each group).
Also note the renaming using AS. You can do that for columns (so your expressions are more compact) as well as for tables (this becomes handy with joins).
For simple GROUP applications, you can shortcut using DISTINCT (which basically computes the “domain").
SELECT DISTINCT ROUND(phot_g_mean_mag), ROUND(parallax) FROM gaiadr1.tgas_source"
Get the averages for the total proper motion from tgas_source in bins of one mag in mag g mean each. Let the output table contain the number of objects in each bin, too.