Yes it is possible to draw histogram with variable bar widths in pgfplots ybar interval, a key for \addplot command.
\documentclass{article}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}[width=10cm,
axis lines=center,
xmin=3,xmax=19,
ymin=0,ymax=3,
grid=major,
yminorgrids,
ylabel near ticks,
xlabel near ticks,
major grid style={thick},
tick style={thick},
axis line style={thick},
xlabel=Age,
ylabel=Frequency density,
xtickmin=4,
xtick={5,6,...,18},
ytick={0,1,2,3},
minor y tick num=3,
axis x discontinuity=crunch,
ticklabel style={font=\tiny},
enlarge x limits={upper,value=0.02},
enlarge y limits={upper,value=0.1}
]
\addplot[ybar interval,fill=red!80!black,draw=white]coordinates{(5,1)(11,3)};
\addplot[ybar interval,fill=orange!80!yellow,draw=white]coordinates{(11,3)(16,2)};
\addplot[ybar interval,fill=cyan,draw=white]coordinates{(16,2)(18,2)};
\end{axis}
\end{tikzpicture}
\end{document}
