1. **State the problem:** We have a grouped frequency table of daily visitors to a gym with class intervals of width 10. We need to calculate the mean number of daily visitors. 2. **Formula for mean of grouped data:** $$\text{Mean} = \frac{\sum f_i x_i}{\sum f_i}$$ where $f_i$ is the frequency of each class interval and $x_i$ is the midpoint of each class interval. 3. **Calculate midpoints $x_i$ for each class interval:** - For 0–<10: $x_1 = \frac{0 + 9}{2} = 4.5$ - For 10–<20: $x_2 = \frac{10 + 19}{2} = 14.5$ - For 20–<30: $x_3 = \frac{20 + 29}{2} = 24.5$ - For 30–<40: $x_4 = \frac{30 + 39}{2} = 34.5$ - For 40–<50: $x_5 = \frac{40 + 49}{2} = 44.5$ - For 50–<60: $x_6 = \frac{50 + 59}{2} = 54.5$ - For 60–<70: $x_7 = \frac{60 + 69}{2} = 64.5$ 4. **Given frequencies $f_i$:** - $f_1 = 5$ - $f_2 = 7$ - $f_3 = 9$ - $f_4 = 8$ - $f_5 = 6$ - $f_6 = 3$ - $f_7 = 2$ 5. **Calculate $f_i x_i$ for each class:** - $5 \times 4.5 = 22.5$ - $7 \times 14.5 = 101.5$ - $9 \times 24.5 = 220.5$ - $8 \times 34.5 = 276$ - $6 \times 44.5 = 267$ - $3 \times 54.5 = 163.5$ - $2 \times 64.5 = 129$ 6. **Sum frequencies and sum of $f_i x_i$:** - $\sum f_i = 5 + 7 + 9 + 8 + 6 + 3 + 2 = 40$ - $\sum f_i x_i = 22.5 + 101.5 + 220.5 + 276 + 267 + 163.5 + 129 = 1180$ 7. **Calculate mean:** $$\text{Mean} = \frac{\sum f_i x_i}{\sum f_i} = \frac{1180}{40}$$ 8. **Simplify fraction:** $$\frac{\cancel{1180}}{\cancel{40}} = \frac{29.5}{1} = 29.5$$ 9. **Interpretation:** The mean number of daily visitors to the gym is 29.5, meaning on average about 30 visitors come daily.