Deciding how to plot data requires thinking about the data and what it might represent. Your illustration showed only three points. If those are all the data that you have, and if there is not some assumed underlying "rule" that suggests a relationship between the points, then you may be best in plotting the data just as isolated points (emphasizing you are making no assumptions about what would be expected for other samples at "in-between" points), or possible a bar graph.
On the other hand, if you think there is a "rule" (such as Y should be a linear function of X, or Y should be a low-order polynomial of X, or Y represents a periodic function of X, or Y is related logarithmically, or exponentially, or via a power law, to X), then you can indulge in some curve-fitting, and once you have a fitting function, you plot the function (which will probably not pass through the points). Note that connecting the points with straight lines is equivalent to saying "I don't know anything about what happens between the points, but I'm confident that at these values of X, Y is the "correct" number, so I'll assume that Y varies linearly as a function of X when I'm between two X values".
In other words, in the absence of a "model", or some idea how the Y values should look at points where you have no measured data, and in the absence of "uncertainty" measures for the X and Y values you are using, isolated points probably represent your data in the "least-misleading" (what a concept!) way, and "connect the dots" is common enough that most readers will intuitively understand that you are "presenting data without a model".
Bob Schor
