In my view, a statistic is nothing more than a mathematical instrument. I had to sit through 4 years of statistics and probability theory. A sample is a sample, a mean is a mean, a standard deviation is a standard deviation, etc.
The 'use' of statistics however can be rediculus when either inappropriate statistical methods are used to reach conclusions, or where conclusions are based upon insufficient or inappropriate or biased data.
For example, I could ask two people I meet in the street there ages, and from this 'conclude' that the average age of Londoners is, say 50. This is clearly a riduculus conclusion, but the statistic that the average age of the sample is 50 is 100% correct.
Most of the rediculus conclusions arise not from the statitics, but from the methodologies by which the samples are drawn, e.g. the sample size is two small, or the sample is biased.