The combination of intrapersonal and interpersonal skills, is said to constitute emotional intelligence (EQ). For those who have a high IQ, say 130 or greater, obtaining a correlation between IQ and EQ is mainly anecdotal because EQ is much more difficult than IQ to measure. Tests such as the MSCEIT, designed to measure emotional intelligence, are difficult to norm because there is a lack of consensus on the best answer to a test item that presents a social simulation.
We do know that many people of high IQ are socially challenged. People like Steve Jobs, Elon Musk, Kurt Gödel, Nikola Tesla and William Shockley are all known for their social friction (interpersonal skills) and/or a lack of self-knowledge (intrapersonal skills). In her book, Extreme Intelligence: Development, Predicaments, Implications, Ph.D. Sonja Falck characterizes two types of extremely intelligent people of low EQ, as “naive child” or “arrogant emperor.” (See: What are some of the signs that someone has high intelligence but low emotional intelligence (EQ)? – Intelligence and IQ )
However, there are many highly intelligent people who also possess high emotional intelligence. Although there is no personality stereotype that can characterize such people, you will usually find that they are self-effacing, rather than self-promoting, open to divergent opinions rather than committed to a specific ideology, and inclusive rather than dismissive. Ben Franklin has often been used as a model of someone who combined emotional intelligence with a high fluid intelligence. Famous physicist Richard Feynman was also regarded by many to have been highly sociable. Katherine Johnson, the woman featured in the movie Hidden Figures is also reported to be a person of high emotional and intellectual strength.
Although we don’t know what proportion of highly intelligent people have also high emotional intelligence, I would conjecture that it would be a large proportion, because emotional intelligence is mainly a learned skill and highly intelligent people are usually excellent at adapting to their environment by learning how to cope. But that is merely a conjecture.