Getting vector statistics in QGIS is very straightforward. The method is similar to raster statistics, although as we can store as many attributes as we want in a vector layer, we can only calculate statistics from a single numeric column at a time. We can access the Show statistical summary tool from the main toolbar (purple Σ button), choose a layer, then choose a numeric column. To save the statistics to a file, we can use QGIS geoalgorithms | Vector table tools | Basic statistics for numeric fields. We can also calculate grouped statistics with QGIS geoalgorithms | Vector table tools | Statistics by categories.