Why could the Tevatron collider only exclude high masses of the Higgs boson? I wish to know why the Tevatron collider could only exclude high masses of the Higgs boson ($158-175~\rm{GeV/c^2}$). The two mainly facts you must to consider are that the Tevatron uses energies off $2~\rm{TeV}$ in mass center and that it collide protons with antiprotons.
 A: A heavy Higgs is easier to detect because it can decay in ways that lead to an easy detection, e.g. in two W or Z bosons. The background processes that lead to the same signature as what you would get if you have a Higgs decaying into two W's are very low, so you don't need to produce all that many Higgs particles to detect it. But at lower masses, there are no such clean signals that stand out well above the background noise, so you need to generate a huge amount of data to be able to filter out the background before the Higgs becomes visible.
To put this in perspective, consider the raw data rate from the Large Hadron Collider:

The raw data per event is around one million bytes (1 Mb), produced at a rate of about 600 million events per second.

This is then filtered in a two stage process:

In the first stage of the selection, the number of events is filtered from the 600 million or so per second picked up by detectors to 100,000 per second sent for digital reconstruction. In a second stage, more specialized algorithms further process the data, leaving only 100 or 200 events of interest per second. This raw data is recorded onto servers at the CERN Data Centre at a rate around 1.5 CDs per second (approximately 1050 megabytes per second). Physicists belonging to worldwide collaborations work continuously to improve detector-calibration methods, and to refine processing algorithms to detect ever more interesting events.

To make sure that this enormous data reduction does not skew the analysis based on the filtered data, a lot of studies had been done in advance where the entire process was simulated. E.g., if you assume a model based on some Higgs mass you can simulate what the raw data would be and then how the filtered data would look like. A statistical analysis on that simulated filtered data should then lead to the Higgs mass that was used as input. 
