From NP: "The starting salary for Diploma in Biomedical Science graduates typically ranges from $1,400 - 1,700 per month."
For degrees from local public universities, you should expect between $1800-2800. $2400 is somewhat the average, for someone with good honours. Salaries for private degree-holders will be slightly lower.
Career-wise, prospect is low with a science degree.
Do make an effort to attend the universities' or polys' openhouses, to find out more about the employment outcomes of their graduates.
So far, what I see is that there's only 3 career pathways for science grads:
1) Join private sector, as a glorified lab tech, aka research assistant. You will have no chance of leading actual research, as the minimum requisite for researchers is a PhD, and PhDs are plentiful in this day and age.
2) Join private sector as a generalist, e.g. customer service.
3) Become a teacher. Apparently 50% of science grads end up working for MOE.
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As for engineering, it is a sunset industry, as Singapore transits to a service economy.
Currently, Singapore has niche areas in the aerospace, marine, pharmaceutical and petroleum sectors. Remunerations for engineers working in these sectors are much better than let's say, civil, mechanical, electrical engineers, who are more often associated with the manufacturing and construction sector, which everyone knows is dominated by cheap foreign talents.
Choose wisely.