Theory

➡ Average or Arithmetic Mean = Sum of all the Values / Total Number of Values
➡ In case of even number of numbers in the set: Median is the mean of the two middle numbers (after the numbers are arranged in the increasing / decreasing order)
➡ In case of odd number of numbers in the set: Median is the middle number (after the numbers are arranged in increasing/ decreasing order )

The arithmetic mean of {6, 1, 11, x, 2} is x

Arithmetic Mean = \(\frac{Sum}{5}\) = \(\frac{6 + 1 + 11 + x + 2}{5}\) = \(\frac{20 + x }{ 5}\) = x (given)
=> 20 + x = 5*x = 5x
=> 5x - x = 20
=> 4x = 20
=> x = \(\frac{20}{4}\) = 5

The median of {2, y, 11, 1, 5} is y

Since there are 5 values and y is the median => y is the middle term or the third term
So, arranging numbers in ascending order and keeping y as the third term we get

{ 1, 2, y, 5, 11 }
Since, y is the median => 2 ≤ y ≤ 5

Clearly Quantity A(x=5) can be greater than or equal to Quantity B (2 ≤ y ≤ 5)

So, Answer will be D.
Hope it helps!

Watch the following video to Learn the Basics of Statistics