Put differently, just because you see a bump, or just because you see a trend, does not mean it is significant and real. It might just be a fluctuation.
When we make claims in public policy or social science, about society, that are empirically grounded, we'll rarely get 5-sigma quality (too few observations, too little theory, too little precision). But, in general, you want to be assured that the claims make sense. Hence you must always attach error bars to your points or claims, where the bars might be 1-sigma plus or minus. Moreover, if you are claiming a trend or a shape, you need to fit the data to see if constancy and a straight line are reasonable zeroth-order assumptions. And if you are making a claim about when something began or the like, there are subtle tests of such in the statistical literature.
Moreover, Bayesian ideas should be on your mind. Even if you have rough measures and not so ideal statistics, can your measurements be seen in the light of what we take as priors and used to revise them. Often, in the policy arena, poor data may still allow you to improve practice, albeit not with the assurance you would like, but at least now you are doing better than without any data and only your presumptions and priors.
Also, never draw a line connecting points unless it is a "fit" to the data. Surely in the case of railroads you can link stations with lines since you know that trains go from A to B to C to... And even here they may not follow straight lines between stations. However, in studying time dependent data, your straight lines presume trends when what you may have is random fluctuation.