3. A. If $a, b$ are given real numbers, and $1<a<b$, then the absolute value of the difference between the average and the median of the four numbers $1, a+1, 2a+b, a+b+1$ is ( ).
(A) 1
(B) $\frac{2a-1}{4}$
(C) $\frac{1}{2}$
(D) $\frac{1}{4}$
3. A. D.

From the given, we know
$$
1<a+1<a+b+1<2 a+b .
$$

Therefore, the average of the four data points is
$$
\begin{array}{l}
\frac{1+(a+1)+(a+b+1)+(2 a+b)}{4} \\
=\frac{3+4 a+2 b}{4},
\end{array}
$$

The median is
$$
\begin{array}{l}
\frac{(a+1)+(a+b+1)}{2}=\frac{4+4 a+2 b}{4} . \\
\text { Then } \frac{4+4 a+2 b}{4}-\frac{3+4 a+2 b}{4}=\frac{1}{4} .
\end{array}
$$