Properly conducted, statistics provide the best analysis of large-number data. Unfortunately, few individuals can perform a rigorous statistical analysis and erroneous conclusions are drawn or at the very least, the data over interpreted.
Case in point, news organizations often present political polling trends of 1 or 2 percentage point drops or increases as if these had any significance. (Most political poles have a margin of error of 3 or 4%.) To report a 1 or 2% change is analogous to tuning a radio a random frequency where no one is broadcasting and turning up the volume, trying to decipher a message from pure white noise.
Thinking about it from a different angle: if set of 100 groups of pollsters, asking the exact same set of questions at exactly the same hour of the day, conducted the same survey, the results would vary by say plus or minus 3.5% That is, there would be at least an 8% difference between the maximum and minimum results for any single question. Moreover, about a third of the 100 surveys would produce answers that are either 3.5% above the average or 3.5% (i.e. 1 standard deviation). It is expected that five surveys would produce that are either 7% above or below the average.
All survey results are equally valid since the exact same survey was given at the same time. The differences in results are simply the inherent random errors of the measurements. The average values from the 100 surveys is likely to be 10 times more accurate than a single one. Thus, the average would still have a 0.35% uncertainty. News organizations are attempting to up their game by taking the averages of perhaps 6 to 9 independent surveys, but those averages are still uncertain by more than 1%, probably more than 2% due to the effects of small number statistics and the mixing of different procedures.
The current discussion has been dealing random errors of repeated measurements. There is often systematic errors in any data. For political polling, systematic errors are injected if there are biases in the questions or if the pollsters fail to sample all demographics correctly.
statistics might not lie, but they don't always say what they appear to be saying. if you take an exit poll after an election and you interview only black women, your statistics will tell what black women exiting THAT polling place choose to say, and if you say that it represents black women everywhere, then the statistics are being USED in a lie. if you say it represents all women, either at that polling place or everywhere, that's a bigger lie. if you say it represents all voters, either at that polling place or everywhere, it's an even bigger lie. statistics can be misstated, misused, misunderstood or gathered in a way that renders them meaningless or deceptive. they can also be lied about deliberately, even if the numbers themselves are not changed (although sometimes they are).
i once read an article about the results of a california study of fraud among welfare recipients. i don't remember the number so please do not take these numbers as anything but place-holders so that i can tell what people did with them. the study found that 30 percent (let's say) of welfare recipients were worthy of being investigated further. of that 30 percent, 10 percent proved to be sufficiently iffy to continue the investigation. of that 10 percent of the 30 percent, one percent turned out to be perpetrating fraud on the system. people took that study and cried "30 percent of welfare recipients in california are committing fraud!" that's dumb but that's what happens. (i repeat, those are not the real numbers; i read this report a few years ago, and i admit that numbers have a tendency to fall out of my head fairly rapidly.)
statistics don't mean anything by themselves. they have to be understood in some kind of context, and they have to be understood correctly. i don't pretend to be able to do that in any more depth than it took to understand my example above, which is a no-brainer (you'd think!) those who can and do are not always honest.