Generally speaking, there isn't a country where the *overall* population is significantly skewed towards one gender or the other.

Globally, the sex ratio at birth is slightly more males than females (around 105 boys for every 100 girls). However, that can change due to mortality rates.

Countries with more males:

• China & India: Historically, these countries have seen skewed sex ratios at birth (more males) due to a combination of factors, including son preference and sex-selective abortions. However, these ratios are slowly improving as awareness and enforcement increase. These are extremely populous countries, so even a small difference makes a huge number of people.
• Countries with large migrant worker populations (especially in the Middle East): Countries like Qatar, the United Arab Emirates, and Saudi Arabia often have a disproportionately high number of male migrant workers, significantly skewing the population towards males. Many of these men are employed in construction and other industries that predominantly hire males.

Countries with more females:

• Russia & other former Soviet Union countries: The gender imbalance here is largely due to the higher mortality rate of men, particularly in middle age. This is linked to factors like alcohol consumption, smoking, risk-taking behaviors, and higher rates of death from accidents and violence. The legacy of wars also contributes to the disparity.
• Some Eastern European countries: Similar to Russia, countries like Latvia, Lithuania, and Belarus have a higher proportion of women, driven by similar factors impacting male mortality.

Understanding sex ratios requires considering more than just the ratio at birth, as overall population demographics are influenced by factors like differing mortality rates between genders, age-specific variations due to lifespan differences, and the accuracy of data collection. Additionally, regional disparities within a country can further complicate the picture, highlighting the need for a nuanced approach when analyzing gender balance.

I also had some research associated with UIUC, below shows the gender demographics of students at the UIUC, based on a report from the Division of Management Information, Institutional Research. Overall, the university has a male majority (54.4% male, 45.4% female), but gender proportions vary significantly across colleges. The School of Social Work is the least gender-diverse undergraduate college with a strong female majority, while Grainger College of Engineering is heavily male-dominated. Within engineering, bioengineering has a female majority, but materials science and engineering has the third-highest proportion of female students at 29.35%. A materials science student notes that the "human side" and biology-related options within the major may attract more women and that a lack of female role models in other engineering departments can be a deterrent.

Reference: https://dailyillini.com/life_and_culture-stories/2021/11/02/gender-diversity-uiuc/ (2021)

One curious thing was that the male portion is larger than the female, as below, and most of them are in Engineering, Gies, Law, and DGS. It looks like there are differences in terms of major interests by the gender.

Reference: https://www.collegefactual.com/colleges/university-of-illinois-at-urbana-champaign/student-life/diversity/