The masters program in statistics at Columbia University is the largest masters program in the United States with just under 300 graduating students per year. What's more, the vast majority of the students are international (Chinese). Many of the classes are taught by adjunct professors, and it's a bit tough to get research experience as a Stats Masters student given the cohort size.
That being said, I think that a domestic applicant with an undergraduate degree from an ivy league institution would be a strong candidate for the program. The "most typical" person in the program is male, Chinese, stats/applied math/engineering major from a Chinese institution, 22 years old (recent college grad), and plans to work as a data scientist in the US. Find a way to differentiate yourself from that.
High scores on the math section of the GRE (General Exam), prior work experience in a quantitative field (almost all of the current students are recent college graduates from a non-US institution), and a strong statement of purpose would strengthen your application. If your math/stats grades are driving down your GPA, I would suggest taking the calculus sequence and linear algebra as a non-degree student before/while you're applying.
As for LOR, academic sources are the most helpful. However, some students were accepted using three non-academic recommenders from their professional experience. To pull that off, you should have been out of school for a long time, and you need to address this in your SOP. Basically state the reasons why a recommendation from your boss is more reflective of your potential as a student than one from some professor you last spoke to half a decade ago.
According to the progam brochure, multivariable calculus and linear algebra are pre-requisites. However, I've seen a handful of cases where students without these can re mediate them in the summer before enrollment or during their first semester. In fact, I've been in classes with people who've been out of school for 5+ years working in finance or marketing, so they took linear algebra and Calc 3 in their first semester.
In summary, high quant GRE scores, solid work experience, a rockstar SOP, and a willingness to remediate the required math courses should mitigate the effects of a low GPA.
Hope this helps.
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