The term 'convulse' has several senses: 1: shake uncontrollably; 2: contract involuntarily, as in a spasm; 3: be overcome with laughter; 4: move or stir about violently; 5: cause to contract; 6: make someone convulse with laughter
Mean can mean you are being rude or in math terms it is adding a set of numbers then dividing by the total amount. ex. If your numbers are 1,2,and 3 add them to get 6 and divide by 3. You get 2.