data = {{2, 1}, {3, 1}, {2, 2}, {5, 1}, {2, 1}, {3, 1}, {7, 1}, {2, 3}, {3,
2}, {2, 1}, {5, 1}};
If you just want to append a pair then use Append or ApendTo
data = Append[data, {8, 4}]
{{2, 1}, {3, 1}, {2, 2}, {5, 1}, {2, 1}, {3, 1}, {7, 1}, {2, 3}, {3,
2}, {2, 1}, {5, 1}, {8, 4}}
data = {{2, 1}, {3, 1}, {2, 2}, {5, 1}, {2, 1}, {3, 1}, {7, 1}, {2, 3}, {3,
2}, {2, 1}, {5, 1}};
AppendTo[data, {8, 4}]
{{2, 1}, {3, 1}, {2, 2}, {5, 1}, {2, 1}, {3, 1}, {7, 1}, {2, 3}, {3,
2}, {2, 1}, {5, 1}, {8, 4}}
% == %%%
True
To select (Take) the first n elements of the data use Take[data, n] where n<= Length[data]
data = {{2, 1}, {3, 1}, {2, 2}, {5, 1}, {2, 1}, {3, 1}, {7, 1}, {2, 3}, {3,
2}, {2, 1}, {5, 1}};
n = 5; Take[data, n]
{{2, 1}, {3, 1}, {2, 2}, {5, 1}, {2, 1}}
If you want to generate a random list of of n pairs
n = 5; RandomInteger[{1, 9}, {n, 2}]
{{9, 4}, {6, 4}, {1, 8}, {6, 3}, {1, 4}}