Even when statistics are technically accurate, particular statistical facts can be very misleading. I once heard a statistic that the rate of teenage pregnancy in a conservative religious group was higher than the national average. This seemed surprising until it became apparent that the reason wasn't a high percentage of unwed mothers - it was a high percentage of women who got married while still in their teens.
I recall hearing apparently conflicting claims about employment during a presidential election campaign a number of years ago. The challenger claimed that unemployment was up during the President's term in office. The President's campaigners said that employment was up! It turns out that both were true. The population had increased, and it turned out the number of people who were employed and the number of people who were unemployed had both increased.