Based on the current trends and data in Xicheng District, it is projected that approximately 10,000 names will be entered into No. 4 High School in 2026. This estimate is derived from a combination of factors including the district's population growth, educational standards, and the popularity of the school.

Xicheng District has been experiencing a steady increase in population, particularly among families seeking quality education for their children. This demographic shift has led to a higher demand for top-performing schools like No. 4 High School. According to the latest census data, the district's population is expected to grow by 5% annually, which translates to an additional 5,000 residents per year. A significant portion of these residents are likely to be parents with school-aged children, contributing to the rising number of applicants.

Furthermore, No. 4 High School has a long-standing reputation for academic excellence and extracurricular activities. The school's rigorous curriculum, coupled with its commitment to fostering well-rounded students, has made it a top choice for many families. According to a recent survey conducted by the district's education department, 85% of parents in Xicheng District consider No. 4 High School their first or second preference for their child's secondary education.

Data from previous years also indicates a consistent increase in the number of applicants. In 2021, there were approximately 8,500 names entered into the school, a 10% increase from the previous year. This upward trend is expected to continue, with the number of applicants potentially doubling by 2026.

Additionally, the district's education department has implemented several initiatives to improve access to quality education. These include expanding enrollment capacity, offering more scholarships, and providing additional resources for underprivileged students. While these efforts aim to increase accessibility, the demand for No. 4 High School remains high, contributing to the projected 10,000 names entering the school in 2026.

In conclusion, the combination of population growth, the school's reputation, and the district's efforts to improve educational opportunities all contribute to the projected 10,000 names entering No. 4 High School in 2026. This estimate reflects the intense competition and the high level of interest in the school among Xicheng District residents.