1. **Problem statement:** We have frequency data of the number of text messages sent by students as follows: - 3 messages: 3 students - 4 messages: 4 students - 5 messages: 8 students - 6 messages: 7 students - 7 messages: 6 students - 8 messages: 3 students We need to find: (a) Total number of students in the class. (b) The median number of text messages sent. (c) The modal number of text messages sent. 2. **(a) Number of students:** Add up all the frequencies: $$3 + 4 + 8 + 7 + 6 + 3 = 31$$ So, there are **31 students** in total. 3. **(b) Median number of text messages:** The total number of students is 31, so the median is the value at the $$\frac{31 + 1}{2} = 16$$th student when ordered by number of messages. List cumulative frequencies: - Up to 3 messages: 3 students - Up to 4 messages: 3 + 4 = 7 students - Up to 5 messages: 7 + 8 = 15 students - Up to 6 messages: 15 + 7 = 22 students The 16th student falls in the 6 messages group because 15 < 16 \leq 22. Thus, the median number of text messages is **6**. 4. **(c) Modal number of text messages:** The mode is the value with the highest frequency. Frequencies: - 3 messages: 3 - 4 messages: 4 - 5 messages: 8 - 6 messages: 7 - 7 messages: 6 - 8 messages: 3 The highest frequency is 8 at 5 messages. So, the mode is **5**. **Final answers:** (a) 31 (b) 6 (c) 5