The correct answer is (c) 6.0.
The arithmetic mean of a set of numbers is the sum of the numbers divided by the number of numbers. In this case, the set of numbers is the first eleven natural numbers, which are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11. The sum of these numbers is 66, and there are 11 numbers in the set. Therefore, the arithmetic mean is 66 / 11 = 6.0.
Option (a), 5.0, is incorrect because the sum of the first eleven natural numbers is 66, which is greater than 50. Option (b), 5.5, is incorrect because the sum of the first eleven natural numbers is 66, which is greater than 55. Option (d), 6.5, is incorrect because the sum of the first eleven natural numbers is 66, which is less than 65.