Promoting positive student attitudes towards stochastics has become a core goal of statistics education reform, and we argue that this starts with the teachers during their teacher preparation program. Building on previous work assessing teachers' attitudes, we focus on how pre-service teacher attitudes vary across different dimensions, and how these patterns can inform teacher training. We present results from assessing attitudes towards stochastics and its teaching for a sample of 269 pre-service Chilean mathematics teachers across three topics: descriptive statistics, probability, and statistical inference. Using a quantitative approach, and considering attitudes towards content and pedagogy, we focus on describing the main attitudinal differences among these three areas. In general, we found positive attitude towards the content and its teaching in all three areas, but with differences among them, primarily in the area of statistical inference. We end with some proposals aimed at improving teacher preparation, focusing on helping pre-service teachers understand the utility and overarching process of statistical investigations.