This is basically a sentence from the answer of Fabian Clermont, but (for beginners) is entered into the code and visualized. In fact, the Ciro Santilli solution is even shorter.
Tested with gnuplot 5.2. For gnuplot 4.6 (OP question time) replace reset session reset and set margin 8,-1,1-1 with set lmargin 8 and set bmargin 1 .
Code:
### Multiplot with single y-label reset session unset key set sample 500 set multiplot layout 7,1 unset ylabel set linetype 1 lc rgb "red" set margins 8,-1,1,-1 # left, right, bottom, top (-1=auto) set ytic 1.0 set title "Plot 1" offset 0,-1 plot sin(1*x) set title "Plot 2" offset 0,-1 plot sin(2*x) set title "Plot 3" offset 0,-1 plot sin(3*x) set title "Plot 4" offset 0,-1 plot sin(4*x) set title "Plot 5" offset 0,-1 plot sin(5*x) set title "Plot 6" offset 0,-1 plot sin(6*x) set title "Plot 7" offset 0,-1 plot sin(7*x) set lmargin -1 # automatic lmargin unset title set origin 0,0 set size 1,1 set border 0 unset tics set ylabel "This is a centered y-label" plot [][0:1] -1 # plot a dummy line out of range unset multiplot ### end of code
Result:

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