1. **Problem Statement:** Arrange the given ages data into a frequency table including class intervals, class marks, tally, frequency, cumulative frequency, and class boundaries. 2. **Formula and Rules:** - Class intervals group data into ranges. - Class mark is the midpoint of each class interval: $\text{Class mark} = \frac{\text{Lower limit} + \text{Upper limit}}{2}$. - Frequency is the count of data points in each class. - Cumulative frequency is the running total of frequencies. - Class boundaries adjust class limits to avoid gaps: lower boundary of first class is lower limit minus 0.5, upper boundary of last class is upper limit plus 0.5, and boundaries between classes are midpoints between upper limit of one class and lower limit of next. 3. **Data Range and Class Intervals:** - Minimum age: 20 - Maximum age: 73 - Choose class intervals of width 10 for simplicity: 20-29, 30-39, 40-49, 50-59, 60-69, 70-79 4. **Calculate Frequencies:** Count ages in each interval: - 20-29: 20,21,22,23,24,28,29 (7) - 30-39: 32,33,33,33,36,37,38,38 (8) - 40-49: 40,40,42,42,42,43,43,43,45,49,49,50 (12) - 50-59: 52,54,54,55,55,56,56,57,57 (9) - 60-69: 60, 64, 65 (3) - 70-79: 70,71,72,72,73,73 (6) 5. **Calculate Class Marks:** - 20-29: $\frac{20+29}{2} = 24.5$ - 30-39: $\frac{30+39}{2} = 34.5$ - 40-49: $\frac{40+49}{2} = 44.5$ - 50-59: $\frac{50+59}{2} = 54.5$ - 60-69: $\frac{60+69}{2} = 64.5$ - 70-79: $\frac{70+79}{2} = 74.5$ 6. **Calculate Cumulative Frequencies:** - 20-29: 7 - 30-39: 7 + 8 = 15 - 40-49: 15 + 12 = 27 - 50-59: 27 + 9 = 36 - 60-69: 36 + 3 = 39 - 70-79: 39 + 6 = 45 7. **Calculate Class Boundaries:** - Lower boundary of first class: $20 - 0.5 = 19.5$ - Upper boundary of first class: $29 + 0.5 = 29.5$ - Similarly for others: - 30-39: 29.5 - 39.5 - 40-49: 39.5 - 49.5 - 50-59: 49.5 - 59.5 - 60-69: 59.5 - 69.5 - 70-79: 69.5 - 79.5 8. **Frequency Table:** | Class Interval | Class Mark | Tally | Frequency | Cumulative Frequency | Class Boundaries | |----------------|------------|-------|-----------|----------------------|------------------| | 20 - 29 | 24.5 | ||||| ||| | 7 | 7 | 19.5 - 29.5 | | 30 - 39 | 34.5 | ||||| || | 8 | 15 | 29.5 - 39.5 | | 40 - 49 | 44.5 | ||||| ||||| ||| | 12 | 27 | 39.5 - 49.5 | | 50 - 59 | 54.5 | ||||| ||| | 9 | 36 | 49.5 - 59.5 | | 60 - 69 | 64.5 | ||| | 3 | 39 | 59.5 - 69.5 | | 70 - 79 | 74.5 | ||||| | 6 | 45 | 69.5 - 79.5 | This completes the frequency table construction for the given data.