How to generalize some data points over time? I have a continuous variable that measures violence in many geographic areas across four time points - four years. 
I want to use this data to say in a simple manner for each region, whether or not - in general - violence is decreasing or increasing over time.
Here is an example of two regions over time:
region1 <- c(340, 330, 550, 320)
region2 <- c(1030, 643, 496, 295)

region2 is very straightforward, it is clearly decreasing substantially over time.
region1 is not so easy to simply explain. It is decreasing slightly over time but also has a large spike in one year.
I am looking for advice regarding how to think about this data and ways in which I can use it to get a general trend for each region. I am hoping a mathematical option might be available to reduce subjectivity in whether or not single outliers in a year are unimportant to the trend.
Thanks for your time and consideration.
 A: I'll need to start with a caveat: this is a complex question that touches on several tricky areas of statistical theory and practice. I don't think it's possible to give a full answer on this forum (and I'm certainly not the person to give that answer). If you're planning to use this information for making important decisions, or you want to publish your conclusions and have them stand up to scrutiny, then you're probably best off hiring a statistical consultant. What I'm presenting here is just a very simplified approach to the problem.
First step is to make sure you're comparing apples to apples - make sure your sources are using comparable definitions of data and measuring it in the same sort of way. Little things like a change to the definition of "violent crime" or how it's reported can make huge differences to the findings. As I noted in my comment above, a lot of crime isn't reported to police, and you'll need to consider how that may affect your inputs.
Once you've done that, your next step is probably going to be to fit a model to the data. The simplest approach would be a linear regression model, using software that gives you uncertainty information or confidence intervals for the slope of the line. The slope of the line will give you information about whether the relevant series is increasing or decreasing over time; the uncertainty in that slope parameter will tell you how reliable that information is.
This assumes that linear regression is an appropriate way to model the data, i.e. that crime stats tend to follow a linear trend over time with normally-distributed "noise". This is not necessarily a good assumption. Crime rates may show non-linear movements and can even change abruptly - for instance, if you decriminalise marijuana, your stats for marijuana offences will drop to zero overnight! Non-normally-distributed errors may also be an issue, especially when you're looking at data based on small counts. 
There are more sophisticated methods designed to handle this sort of issue: time-series analysis, non-parametric regression, etc. etc. Unfortunately, to the best of my knowledge, none of them are likely to give much information on such a short time series. Even if you accept the assumptions and limitations of linear regression, you will quite likely find that there's a lot of uncertainty in your trend estimates, because four points just isn't much to work with. Are you able to get a longer time series?
Apologies for giving an answer that's probably rather less helpful than you were hoping for. Unfortunately, this is a tough problem!
A: You need some how to be able to represent numbers for each region which is saying that the violence in the last X years decreases or better then , I will take your current example and will try to think with you together :
The difference/change between numbers/number of violence in ea year : 
region1 : 10,-220,230
region2 : 387,147,201
Now , Lets take the number of times there was positive/negative change and the total change size:
region1 : 2 positive = 230+10= 240, 1 negative = 220
 region2 : 4 positive = 387+147+147+201 = 882 , 0 negative = 0 
Now we can average and say something about each region :
region1 in the last 4 years had ~ 240/2= 120 positive changes and ~220 negative changes.
region2 in the last 4 years had ~ 882/4 = 220 positive changes and ~0 negative changes.
conclusion :
The total change for region 1 : ~120-220 = -100
The total change for region 2 : ~220
region 1 is more violent then region 2.
Now....I know this is not exactly what you are looking for but this can give you some sense about which way you should look for (:  
