use Data::Table;

$header[0] = "NAME";  $header[1] = "NUMBER";

$data[0][0] = "Mary";  $data[0][1] = 3;
$data[1][0] = "John";  $data[1][1] = 2;
$data[2][0] = "John";  $data[2][0] = 4;
$data[3][0] = "Mary";  $data[3][1] = 2;

$table = new Data::Table ($data, $header, 0);

# TRIPLETS, FIRST PARAM IS COLUMN INDEX, SECOND IS NUMERICAL VALUE/ 
# NON-NUMERICAL, THIRD IS ASCENDING/DESCENDING SORT
$table->sort(0, 1, 0, 1, 0, 0);

# RECONSTITUTE ARRAY
$data[0][0] = $table->elm(0,0);  $data[0][1] = $table->elm(0,1);
$data[1][0] = $table->elm(1,0);  $data[1][1] = $table->elm(1,1);
$data[2][0] = $table->elm(2,0);  $data[2][1] = $table->elm(2,1);
$data[3][0] = $table->elm(3,0);  $data[3][1] = $table->elm(3,1);

print "$header[0]\t$header[1]\n\n";
print "$data[0][0]\t$data[0][1]\n";
print "$data[1][0]\t$data[1][1]\n";
print "$data[2][0]\t$data[2][1]\n";
print "$data[3][0]\t$data[3][1]\n";
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Thanks again, cypress

(And I did make a slight data typo in my original post.)

You should start by using strict and warnings. And if you did, you might have spotted this. Note that you are assigning values to elements of the array @data and the constructing the object Data::Table with the scalar $data which does not relate to the array, and it is not the array reference the constructor is expecting. The same applies to @header.