Getting tabular statistics from table using QGIS?
Statist plugin is going to be your friend here:
IMHO - it beats ESRI approach hands down with both functionality and aesthetics.
For looking at groupings of your data I'd also recommend Group Stats plugin:
Although (afaik) it doesn't work with single variables, it comes really handy for getting quick summaries of most important parameters of distribution of certain variable across groups of other variable. And yet again - ESRI is far beyond here.
I've also seen Spqr out there, but haven't had chance to give it a proper spin. It works with R and looks really promising, but seems to be still in early days, and as author suggests it is:
For experts and crazy people only. Bits of this aren't implemented and other bits don't work and most of it will break if you push it.
Years later, I had the same question with QGIS 2.18.16, and I came across this thread.
The QGIS alternative to the Arc Frequency tool is:
Toolbox > QGIS Geoalgorithms > Vector table tools > Frequency Analysis
there is also the tool statistic by categories beside the tool basic statistics. It is similar to the one in ArcGIS where you can get statistics for fields one based on another