Data Science is at the intersection of Computer Science (Computer Engineering, Statistics, Functional Management (like Marketing, Finance, Supply Chain etc.) and business domain (eg BFSI, FMCG, DeepTech and so on). It is not practical to have skills and qualifications on all of these and therefore, earlier on, it is desirable to have a plan based on own competencies, likeness.

Data Science as a functional area has been ruled by professionals with qualifications in computer science and/or statistics-mathematics. The core foundation of data science is primarily mathematics, and therefore without a flair for mathematics or say interest in mathematics, one is not expected to do well in this field. It is interesting to note that the foundation of computer science and statistics is also mathematics. 

It has been experienced in India (and elsewhere) that due to pressure (often from family/peer group), students take up their undergraduate studies in a non-STEM (science technology engineering mathematics) field like commerce or business administration etc. Quite often, since securing a position as an undergraduate student in a decent Stem programme requires going through difficult entrance exams after high school, a student might find oneself over-whelmed and underprepared. There could be other different reasons for such early career decisions.

With this in the background, I will mention specific two cases of transition to data science from a non-STEM background from my own experience: 

(a) An undergrad business student moving successfully to data science and finally getting admitted to MS Computer Science Engineering is one of the top 20 universities in the USA, in New York 

(b) An undergrad in Hotel Management pursued one of our graduate courses in data science and making it to one of the top 3 analytics companies in India and currently being hired as a software engineer for a Boston based fintech company. 

In both cases, the students wanted to have a job right after the undergrad degree and they were advised to pursue the above programs by their parents/peers/counsellors, whereas their interest was in computer science. Data Science though heavily dependent on computer science and statistics at an academic level (both for UG and PG) preparing students for an entry-level position in the IT/Analytics department of a company, does accommodate such cases since the entry requirement is not yet so well-defined as would have been for an engineering master. In both the cases above, the students had a flair for coding, mathematics and hence when they got an opportunity to prove themselves, they flourished. 

Therefore, yes it is possible for a non-Stem student to pursue Data Science at an undergrad or grad level provided, they have a genuine interest in the subject.

There are several companies, private entrepreneur education ventures which often counsel students that one does not have to code, no need to go through complex algebra and calculus, no need to know the basics of databases (relational or columnar): these are not true. There is no serious data scientist in the world who does not know coding and stats: the two fundamental qualifications in data science. If one looks back some 15-20 years in India and elsewhere, several universities started offering undergrad courses in Computer Science, because with a CS degree one could aspire to get a position as a fresher, easily. In the case of India, where family resources are stretched to accommodate college education for a member, getting a job after the program becomes a priority. Thousands of students ended up with Computer Science degrees, but with a fundamental flaw – most could not write a decent line of code. As a result, beyond mass-recruiting ITES companies, they could hardly find a job in companies where they probably had aspired to work.

A hard technical subject like data science would definitely need a genuine interest in computer science at a foundation level and there is no escape from this stark reality. It won’t matter if the student has done his undergrad in another subject that is non-Stem, but as the space of demand-supply is closing over the next few years, one seriously need to consider his/her own mojo before signing up with a course that could probably give a lift in career; but without real interest in the field, one would not be able to keep the job for long and would probably need to move to allied fields like marketing analytics, MIS reporting etc. where you don’t need to know list and tuples, neither you need to understand a principal component of a neural network – but to crunch the data in a spreadsheet. That’s not data science, unfortunately.