The hypothesis that blood cholesterol levels are positively correlated with heart disease (the lipid hypothesis) dates back to Rudolph Virchow in the mid-1800s.
One famous study that supported this hypothesis was Ancel Keys's Seven Countries Study, conducted between the 1950s and 1970s. This study eventually served as the foundation on which much of the advice that we receive today from doctors is based, even though several other studies have been published since that provide little support for the lipid hypothesis.
The graph below (source: canibaisereis.com, with many thanks to O Primitivo) shows the results of one study, involving many more countries than Key's Seven Countries Study, that actually suggests a NEGATIVE linear correlation between total cholesterol and cardiovascular disease.
Now, most relationships in nature are nonlinear, with quite a few following a pattern that looks like a U-curve (plain or inverted); sometimes called a J-curve pattern. The graph below (source also: canibaisereis.com) shows the U-curve relationship between total cholesterol and mortality, with cardiovascular disease mortality indicated through a dotted red line at the bottom.
The total mortality curve is the one indicated through the full blue line at the top. In fact, it suggests that mortality increases sharply as TC decreases below 200.
Now, these graphs relate TC with disease and mortality, and say nothing about LDL cholesterol (LDL). In my own experience, and that of many people I know, a TC of about 200 will typically be associated with a slightly elevated LDL (e.g., 110 to 150), even if one has a high HDL cholesterol (i.e., greater than 60).
Yet, most people who have a LDL greater than 100 will be told by their doctors, usually with the best of the intentions, to take statins, so that they can "keep their LDL under control". (LDL levels are usually calculated, not measured directly, which itself creates a whole new set of problems.)
Alas, reducing LDL to 100 or less will typically reduce TC below 200. If we go by the graphs above, especially the one showing the U-curves, these folks' risk for cardiovascular disease and mortality will go up - exactly the opposite effect that they and their doctors expected. And that will cost them financially as well, as statin drugs are expensive, in part to pay for all those TV ads.