# What's a simple way to test for a break in a small sample time-series?

I have 10 observations of yearly annual housing price data for hundreds of cities.

If I wanted to detect data entry or reporting errors for each city series, what would be the simplest test to run in order to say that year 'x' of city XYZ has a potential structural break?

I worry that my small sample size per city (n=10) will be an issue.

You can use a changepoint algorithm. I use the changepoint package in R. It will detect a change in the mean, variance, or mean and variance. Sample size isn't an issue, in terms of requirements of the algorithm.
I just gave an overview on using changepoint's functions here on a different question. Check that out if your interested in doing it in R and I talk about potential choices of method and parameters.