<p>Based on Harvard’s FAQ webpage, approximately one-third of all undergraduates switch majors. I would assume that it is a bit higher among those intending to concentrate in the sciences even though it would be fairly reasonable to posit that the switch would most often be from one math/science major to another.</p>
<p>[Harvard</a> College Admissions § About Harvard: Frequently Asked Questions](<a href=“http://www.admissions.college.harvard.edu/about/faq.html#7]Harvard”>http://www.admissions.college.harvard.edu/about/faq.html#7)</p>