How statistics can be misused in reporting of concern to the population?

Statistical analysis is used to extend our knowledge of a particular phenomena or process. It is used in decision making. It is particularly useful when the analysis is consistent with our theoretical or conceptual understanding of a phenomena.

I will give you a simple example. We design a coin to be as perfectly balanced as possible. We flip the coin a thousand times, and it comes up heads just about exactly 50% of the time.

Now, not all research is as simple as coin flipping. A less than complete list of all possibilities or outcomes can lead to erroneous conclusions. Note the example given on the attached link. A statistician concludes that people with 2 tickets or more are poor drivers and likely to be involved in more accidents. He does not consider that drivers with two or more tickets might just drive more. Also, the drivers with tickets may drive on roads where they are more likely to get tickets for traffic infractions.

Observational studies can have critical flaws by not considering all data. A real example is a study conducted by the US Fish and Wildlife Department to evaluate the distance that the Florida Panther would roam in the Everglades National Park. They were able to tag the panthers and track their movements by satellite. By using only day time data (when the panthers sleep) , they underestimated the distance a panther would roam.

The related links give a number of examples of the misuse of statistics. I've also included a link to the book, "How to Lie with Statistics", which has far outlasted most books on statistics.