1. **State the problem:** We have a frequency distribution of the number of texts sent by students in intervals and the number of students in each interval. We need to find: (a) The total number of students in the group. (b) The mean number of texts sent per month using mid-interval values. 2. **Calculate total number of students:** Add the number of students in each interval: $$12 + 18 + 22 + 10 + 8 = 70$$ So, there are 70 students in total. 3. **Find mid-interval values:** For each interval, the mid-interval value is the average of the lower and upper bounds: - 0–50: $\frac{0 + 50}{2} = 25$ - 50–100: $\frac{50 + 100}{2} = 75$ - 100–150: $\frac{100 + 150}{2} = 125$ - 150–200: $\frac{150 + 200}{2} = 175$ - 200–250: $\frac{200 + 250}{2} = 225$ 4. **Calculate weighted sum of texts:** Multiply each mid-interval value by the number of students in that interval: $$25 \times 12 = 300$$ $$75 \times 18 = 1350$$ $$125 \times 22 = 2750$$ $$175 \times 10 = 1750$$ $$225 \times 8 = 1800$$ 5. **Sum the weighted values:** $$300 + 1350 + 2750 + 1750 + 1800 = 7950$$ 6. **Calculate the mean number of texts:** $$\text{Mean} = \frac{\text{Total weighted texts}}{\text{Total students}} = \frac{7950}{70}$$ Show cancellation step: $$\frac{\cancel{7950}}{\cancel{70}} = \frac{7950 \div 10}{70 \div 10} = \frac{795}{7}$$ Calculate division: $$\frac{795}{7} = 113.57$$ (rounded to two decimal places) 7. **Final answer:** (a) Total students = 70 (b) Mean number of texts sent per month $\approx 113.57$ texts