Statistics + Computer Science = Data Science?
Well it depends on what kind of "Data Science" you wish to get in to.  For basic analytics and reporting statistics will certainly help, but for Machine Learning and Artificial Intelligence then you'll want a few more skills


Probability theory - you must have a solid background in pure probability so that you can decompose any problem, whether seen before or not, into probabilistic principles.  Statistics helps a lot for already solved problems, but new and unsolved problems require a deep understanding of probability so that you can design appropriate techniques.
Information Theory - this (relative to statistics) is quite a new field (though still decades old), the most important work was by Shannon, but even more important and often neglected note in literature is work by Hobson that proved that Kullback-Leibler Divergence is the only mathematical definition that truly captures the notion of a "measure of information". Now fundamental to artificial intellgence is being able to quantify information.  Suggest reading "Concepts in Statistical Mechanics" - Arthur Hobson (very expensive book, only available in academic libraries).
Complexity Theory - A big problem many Data Scientists face that do not have a solid complexity theory background is that their algorithms do not scale, or just take an extremely long time to run on large data.  Take PCA for example, many peoples favourite answer to the interview question "how do you reduce the number of features in our dataset", but even if you tell the candidate "the data set is really really really large" they still propose various forms of PCA that are O(n^3).  If you want to stand out, you want to be able to solve each problem on it's own, NOT throw some text book solution at it designed a long time ago before Big Data was such a hip thing.  For that you need to understand how long things take to run, not only theoretically, but practically - so how to use a cluster of computers to distribute an algorithm, or which data structures take up less memory.
Communication Skills - A huge part of Data Science is understanding business.  Whether it's inventing a product driven by data science, or giving business insight driven by data science, being able to communicate well with both the Project and Product Managers, the tech teams, and your fellow data scientists is very important.  You can have an amazing idea, say an awesome AI solution, but if you cannot effectively (a) communicate WHY that will make the business money, (b) convince your collegues it will work and (c) explain to tech people how you need their help to build it, then it wont get done.