How to plot data without a separate file by specifying all points inside the Gnuplot script?

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You can use the syntax for inline data – filename '-'.

The following example produces a simple plot in a GIF image (bash script):

gnuplot << EOF
set terminal gif
set output 'plot1.gif'
plot '-' using 1:2
        1 10
        2 20
        3 32
        4 40
        5 50
        e
EOF

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