The relationship between the number of items N and the cost per item C is an inverse variation. If (1, y), (2, 11), and (4, x) are pairs of values for (N, C), what is x/y?

We use the complete pair $(N, C) = (2, 11)$ to find $k$:

$$k = 2 \times 11$$ $$k = 22$$

Using the pair $(N, C) = (1, y)$ and the constant $k=22$:

$$1 \times y = 22$$ $$y = 22$$

Using the pair $(N, C) = (4, x)$ and the constant $k=22$:

$$4 \times x = 22$$ $$x = \frac{22}{4}$$ $$x = \frac{11}{2}$$

Now we substitute the values of $x$ and $y$ into the expression $\frac{x}{y}$:

$$\frac{x}{y} = \frac{\frac{11}{2}}{22}$$

To simplify, we multiply the numerator by the reciprocal of the denominator:

$$\frac{x}{y} = \frac{11}{2} \times \frac{1}{22}$$ $$\frac{x}{y} = \frac{11}{44}$$ $$\frac{x}{y} = \frac{1}{4}$$

The phrase "if the mean number is 2/6" is ambiguous and does not seem to relate to the inverse variation data in a consistent way. Therefore, we proceed with the calculation based on the inverse variation as the primary instruction.

The final answer is $\frac{1}{4}$.