Apparently, Trump's claimed IQ isn't actually official. It is based on an out-of-date, no longer accepted estimation based on SAT scores and Trump's acceptance to Wharton. But, in this case, Trump transferred to Wharton late, and the SAT standard wouldn't be appropriate in his case, even if it was still accepted.
So, Trump's claim and that of the psychologist mentioned below aren't convincing in the least.
Fact Check: How smart is President-elect Donald Trump? IQ score isn’t official
The chart is based on a real university study by a real psychologist, but the claim that Trump has an IQ of 156 is not. This rumor has been around since at least August 2015, when the website BeforeItsNews.com published an article with an estimation of his IQ:
“Donald Trump graduated from the Wharton School at the University of Pennsylvania in 1968, with a Bachelor of Science degree in economics and anthropology. Mensa doesn’t accept SAT scores from after 1994. However, Mr. Trump was a student at Wharton when it was possible to derive an accurate IQ core from known SAT scores. Given the usual requirements for admission to a top school like Wharton, I estimate that Mr. Trump has a 156 IQ at the minimum.
“The standard description of this level of intelligence is ‘Genius — Exceptional intellectual ability and capable of looking beyond known facts.’ However, the percentile rating is more revealing than the raw score. A 156 IQ is at the 99.9905490555 percentile. That means that Donald Trump is smarter than 99.99 percent of the people on planet Earth. Not only does Trump qualify for membership in Mensa, but he could join the Triple Nine Society [people scoring at or above the 99.9th percentile on selected intelligence tests].”
Snopes.com points out that the article in BeforeItsNews.com — a site consisting of anyone who wants to report on what’s going on around them — is full of illogical conclusions. Trump’s official school transcripts are not available, so it is impossible to know his actual scholastic aptitude scores. While the article’s author used Wharton’s general admission requirements to estimate Trump’s IQ, the math still doesn’t quite add up.
PrepScholar.com states that Wharton’s SAT requirements are currently 1500. This roughly translates to an IQ score between 145 and 149, not 156. Regardless, Wharton’s admission requirements are irrelevant, since Trump did not enter Wharton as a freshman. He transferred there his junior year, and Wharton does not list SAT scores among its requirements for transfer students, Snopes.com reports.
So, even though the IQ chart is based on a real study, it’s still just estimation. And there is no way to know what Trump’s IQ is.