1. **Problem 1: Filling tally and frequency for swimming lengths** - Given responses: 22, 75, 45, 28, 74, 53, 63, 38, 43, 34, 24, 63, 29 - Intervals: 0-24 (A), 25-49 (B), 50-74 (C), 75-99 (D) - Count frequencies: - 0-24: 22, 24 → 2 responses - 25-49: 28, 29, 34, 38, 43, 45 → 6 responses - 50-74: 53, 63, 63, 74, 75 → 5 responses - 75-99: 75 → 1 response (75 is in 75-99) - Tally marks: - A: || - B: |||||| - C: ||||| - D: | 2. **Problem 2: Completing vehicle sales table** - Table given: | | Motorbike | Car | Van | Total | | Petrol | ? | 2 | 5 | ? | | Diesel | ? | ? | ? | 11 | | Electric | 4 | ? | 3 | 9 | | Total | ? | 10 | ? | 30 | - Use totals to find missing values: - Car total = 10, Petrol car = 2, so Electric car = 10 - 2 = 8 - Electric total = 9, Electric motorbike = 4, Electric van = 3, Electric car = 8 (contradiction) - Sum Electric row: 4 + 8 + 3 = 15, but total given is 9 → inconsistent data - Conclusion: Cannot complete table with given data; need consistent totals or missing values. 3. **Problem 3: Which tally chart is better?** - Chart A uses standard tally marks grouped in fives, easy to count. - Chart B uses stylized tally marks (HH II I), less standard and harder to interpret. - Better chart: Chart A, because it is clearer and more universally understood. 4. **Problem 4: Fraction of tennis club members aged 30 to 39** - Total tennis members = 20 - Members aged 30 to 39 = 14 - Fraction = $\frac{14}{20} = \frac{7}{10}$ after simplification. 5. **Problem 5: Drawing tally chart for pet ownership** - Responses not visible, so cannot draw tally chart. 6. **Problem 6: Games City FC lost** - Total games City FC played = 35 - Wins = 12 - Draws unknown, but total draws = 40, Town Rovers draws = 8, Club United draws unknown - Losses City FC = Total games - Wins - Draws - From table, City FC losses = 35 - 12 - (unknown draws) - Given total losses for Club United = 7, total games = 90 - Without draws for City FC, cannot find exact losses. 7. **Problem 7: Best use of tally chart** - A: Height changes each year - continuous data, not suitable. - B: Favourite music types - categorical data, suitable. - C: Names of people - nominal data, but tally charts not ideal. - Best choice: B