As commented by @Vince in(in response to you commenting that "It is not the csv that I want to edit. Rather it is the .lyr file called statistical_areas_2011""It is not the csv that I want to edit. Rather it is the .lyr file called statistical_areas_2011"):
Layer files do not contain data. They just point at the actual data source. In order to edit data, the data format must be editable by ArcGIS, the license level of ArcGIS must support editing of that format, and you must have read-write access to the data source. I much prefer to use the layer context menu to choose the source for editing.