The histogram displays the number of students based on how much time they spent on mathematics homework. To determine the total number of students surveyed, we need to add the frequencies represented by the histogram bars. Here's how you calculate it:

1. Each bar represents a range of time and the number of students in that range:

   • 10–15 minutes: 1 student
   • 15–20 minutes: 3 students
   • 20–25 minutes: 6 students
   • 25–30 minutes: 5 students
   • 30–35 minutes: 4 students

2. Add these frequencies together: $1 + 3 + 6 + 5 + 4 = 19$

Thus, 19 students were surveyed.

Would you like further clarification or analysis of this data? Here are five related questions to consider:

1. What is the most common range of time spent on homework?
2. What percentage of students spent 20–25 minutes on homework?
3. What is the average time spent on homework by the students?
4. How can this data help the teacher adjust homework assignments?
5. Could we group the time intervals differently to see a different pattern?

Tip: When interpreting histograms, ensure to carefully examine the frequency for each range and check the axis labels to avoid misreading the data.