zonalstats = qgis.analysis.QgsZonalStatistics(vectorlayer,rasterfile)
    zonalstats.calculateStatistics(None)

calculates by default just Count, Sum and Mean (as you can tell from `Raster -> Zonal Statistics` in QGIS Desktop, it can do a lot more).

If you, for instance, want to compute just the Mean you have to use:

    zonalstats = qgis.analysis.QgsZonalStatistics(vectorlayer, rasterfile, QgsZonalStatistics.Mean())
    zonalstats.calculateStatistics(None)

see [API][1] for all options.


  [1]: http://qgis.org/api/classQgsZonalStatistics.html#details "API"