Discuss how you have seen statistics used to mislead in your work or life. How do you (or would you) now critically analyze statistical evidence rather than accepting it as true and representative?
Politicians are regular abusers of statistics, as you just need a statistician to manipulate the figures to come up with statistics that will prove your point, whatever reality actually says. Statistics are often used to mislead the general public in this way, as politicians will give us statistics that only support what they are trying to prove or argue than statistics that accurately reflect reality.
Education statistics, in particular standardized test scores, are often misleading because they seldom focus on student growth. The public hears that a certain percentage of students were not at grade level, but not any gains they may have made.
Polling data, particularly that used on some of the news outlets that brettd referenced above, can also be profoundly misleading, as the terms of the question often dictate the answer.
We're seeing statistics misused in two directions tonight, when reporting on the results of the New Hampshire primary election. Mitt Romney is being declared a convincing winner, with approximately 37% of the vote, far below half and a fairly weak plurality. On the other hand, you have left-leaning news outlets reporting or posting that two out of three Republicans voted against Mitt Romney. Perhaps that's not really misleading as much as it is opportunistic.
We also often hear statistics about how American students don't perform well when compared against other countries, except America's education system is decidedly different. We educate everyone, with open enrollment and 5th year seniors included, while European schools track heavily so that college bound students are most of what's left at the senior level. Compare using only American AP student test results instead and America's standing in the world improves dramatically.
In many states, school districts use statistics concerning student achievement to evaluate the performance of the teacher. This can be misleading in many ways: Some teachers have classes full of low-ability and poorly performing students, while other teachers are blessed with a full class of over-achievers. Statistics in such a case might tend to show that the teacher with the over-achievers is a better teacher--and due a higher evaluation score--than the instructor with the low-achievers which, in reality, might not be the case at all.
I would agree that a person needs to be very cautious when examining statistics. Some people simply accept things as they are without questioning them. (Think about pharmaceutical companies and the statistics they provide the public at large with.) Many statistics are provided to sway the public in one direction or another.
One of the most important things to do when trying to determine if statistics are accurate or not is to look at their source. You have to be able to evaluate sources and see if they are likely to be biased. In Post #2's example, you would assume that any statistic given by the Romney campaign about his job creation is likely to be high while any statistics given on the same issue by the Gingrich campaign would be too low.
Statistics are often used in misleading ways in political debates, especially on the national level. There is, for instance, presently a debate about how many jobs Mitt Romney did or did not create while working in the private sector. There is a similar debate regarding the growth of jobs during Rick Perry's service as Governor of Texas. Even the most recent statistics relating to the fall in the U. S. unemployment rate have been challenged.
It's very difficult for individuals to know the "truth" or reliability of statistical claims. The rise of "fact checking" sites on the internet has been helpful, although even their objectivity and reliability has been challenged!