You can add a new plot with a different plot type by using \addplot [<plot type>] ...;.
If you want to add a line plot to a column plot, you would use \addplot [sharp plot] ...;.
If you want to keep the current color cycle uninterrupted, add a + in front of the options: \addplot +[sharp plot] ...;
To calculate the cumulated sums automatically, you can make use of the PGFplotstable package that ships with PGFplots. It allows you to save data into tables which can then be fed to PGFplots using \addplot table {<\tablemacro>}. You create the table using
\pgfplotstableread{ Answer Count no 7 yes 3 undecided 1 }\results
where the first data line is the header that assigns the column names, and the \results is the macro the table is saved to. To create a new column that contains the cumulated results, you issue
\pgfplotstableset{ create on use/Cumulated/.style={ create col/expr={ \pgfmathaccuma + \thisrow{Count} } } }
which tells PGFplotstable that whenever you access the column Cumulated (which does not exist yet), it will automatically create a new column consisting of the sum of \pgfmathaccuma (initially empty) and the current value of Count.
In your plot, you would then just say
\addplot [sharp plot] table [y=Cumulated] {\results};

Here's the complete code:
\documentclass[11pt]{amsart} \usepackage{pgfplots} \usepackage{pgfplotstable} \begin{document} \pgfplotstableread{ Answer Count no 7 yes 3 undecided 1 }\results \pgfplotstableset{ create on use/Cumulated/.style={ create col/expr={ \pgfmathaccuma + \thisrow{Count} } } } \begin{tikzpicture} \begin{axis}[ ybar, ymin=0, ylabel={\#participants}, symbolic x coords={no,yes,undecided}, xtick=data ] \addplot [fill=gray!30, nodes near coords] table {\results}; \addplot [sharp plot,mark=*] table [y=Cumulated] {\results}; \end{axis} \end{tikzpicture} \end{document}