<p>Measure theory abstracts from both calculus and statistics. The central object of study is that of a measure space (just some collection of points, discreet or not) which is endowed with a measure function (this could be a probability density function or a volume element). In this framework one can prove theorems that apply to calculus and statistics and a whole lot of other areas. In this sense calculus and statistics (or at least probability theory) can both be classified under the same branch of mathematics.</p>
<p>If calculus is necessary for certain statistics applications is another question entirely.</p>