Drawing vertical lines from given x-axis values to frequency curve intersections, then to the y axis

The same strategy as under the previous thread works: add paths and compute intersections.

documentclass{article}
usepackage{pgfplots}
usepackage{pgfplotstable}
usetikzlibrary{intersections}
pgfplotsset{compat=1.17}


begin{document}
begin{figure}
centering
begin{tikzpicture}
begin{axis}[tick align=outside,tick pos=lower,width=11cm,
xtick={10,20,...,100},xticklabel=empty,
minor tick style={draw=none},x tick style={draw=none},
extra x ticks={9.5,19.5,...,99.5},
extra x tick style={draw,ultra thick,grid style={draw=none},x tick style={draw},
xticklabel=pgfmathprintnumbertick,
xticklabel style={rotate=30}},
axis x line=bottom,axis y line=left, 
xmin=9,xmax=100,xlabel=Marks,
ymin=0,ymax=55,minor tick num=4,ylabel=Cumulative frequency,
grid=both,grid style={cyan},minor grid style={help lines,cyan},
table/create on use/cumulative frequency/.style={% cf. https://tex.stackexchange.com/a/198397
create col/expr={pgfmathaccuma + thisrow{frequency}} 
}]
addplot[red,thick,name path=plot,smooth,mark=+,mark options={color=black}] 
table [x expr=9.5+10*coordindex,
y=cumulative frequency]{
frequency
2
3
4
6
13
10
5
3
2
2
} coordinate[pos=1](pmax);
path (0,0) coordinate (O)
(100,0) coordinate (br) (100,pgfkeysvalueof{/pgfplots/ymax}) coordinate
(tr); 
pgfplotsinvokeforeach{42,76}{%
path[name path=v#1] (#1,0) coordinate (x#1)-- (x#1|-pmax);
path[name intersections={of=v#1 and plot,by=i#1}];}
end{axis}
draw[-stealth] (br) -- (tr);
path (br) -- (br|-pmax) foreach X in {0,20,...,100}
{coordinate[pos=X/100] (pX)
(pX) edge[help lines]++ (pgfkeysvalueof{/pgfplots/minor tick length},0)
node[pos=X/100,right,xshift=pgfkeysvalueof{/pgfplots/minor tick length}] {X%} };
foreach X in {42,76}
{draw[dashed,semithick] (xX) |- (br|-iX) node[right]{$v_{X}$};}
end{tikzpicture}
end{figure}
end{document}

Please note that the figure was too wide for the article document class you have chosen, so I decreased the width. (The options tikz,border=3mm work for standalone but are not options of the article class.)

ADDENDUM:

documentclass{article}
usepackage{pgfplots}
usepackage{pgfplotstable}
usetikzlibrary{intersections}
pgfplotsset{compat=1.17}


begin{document}
begin{figure}
centering
begin{tikzpicture}
begin{axis}[tick align=outside,tick pos=lower,width=11cm,
xtick={10,20,...,100},xticklabel=empty,
minor tick style={draw=none},x tick style={draw=none},
extra x ticks={9.5,19.5,...,99.5},
extra x tick style={draw,ultra thick,grid style={draw=none},x tick style={draw},
xticklabel=pgfmathprintnumbertick,
xticklabel style={rotate=30}},
axis x line=bottom,axis y line=left, 
xmin=9,xmax=100,xlabel=Marks,
ymin=0,ymax=55,minor tick num=4,ylabel=Cumulative frequency,
grid=both,grid style={cyan},minor grid style={help lines,cyan},
table/create on use/cumulative frequency/.style={% cf. https://tex.stackexchange.com/a/198397
create col/expr={pgfmathaccuma + thisrow{frequency}} 
}]
addplot[red,thick,name path=plot,smooth,mark=+,mark options={color=black}] 
table [x expr=9.5+10*coordindex,
y=cumulative frequency]{
frequency
2
3
4
6
13
10
5
3
2
2
} coordinate[pos=1](pmax);
path (0,0) coordinate (O) (9.5,0) coordinate (O')
(100,0) coordinate (br) (100,pgfkeysvalueof{/pgfplots/ymax}) coordinate
(tr); 
pgfplotsinvokeforeach{42,76}{%
path[name path=v#1] (#1,0) coordinate (x#1)-- (x#1|-pmax);
path[name intersections={of=v#1 and plot,by=i#1}];}
end{axis}
draw[-stealth] (br) -- (tr);
path (br) -- (br|-pmax) foreach X in {0,20,...,100}
{coordinate[pos=X/100] (pX)
(pX) edge[help lines]++ (pgfkeysvalueof{/pgfplots/minor tick length},0)
node[pos=X/100,right,xshift=pgfkeysvalueof{/pgfplots/minor tick length}] {X%} };
foreach X in {42,76}
{draw[dashed,semithick] (xX) |- (O'|-iX) node[left]{$v_{X}$};}
end{tikzpicture}
end{figure}
end{document}