1. **Problem:** Create a histogram for the ages of 60 people using Sturges' Rule. 2. **Formula:** Sturges' Rule for number of classes $k$ is: $$k = 1 + \log_2(n)$$ where $n$ is the number of observations. 3. **Calculate number of classes (k):** $$k = 1 + \log_2(60) \approx 1 + 5.9069 = 6.9069 \approx 7$$ So, $k = 7$ classes. 4. **Determine class width:** Find the range: $$\text{Range} = \text{max} - \text{min} = 200 - 18 = 182$$ Class width $w$ is: $$w = \frac{\text{Range}}{k} = \frac{182}{7} = 26$$ 5. **Create class intervals:** Start from 18, add class width 26 each time: - 18 - 43 - 44 - 69 - 70 - 95 - 96 - 121 - 122 - 147 - 148 - 173 - 174 - 199 6. **Frequency distribution table:** Count how many ages fall into each interval: - 18-43: 7 (18,22,25,30,34,38,42) - 44-69: 6 (45,50,53,55,60,62,65) - 70-95: 7 (70,72,75,78,80,82,85,88,90,92,95) actually 11, corrected count - 96-121: 5 (98,100,105,110,112,115,118,120) actually 8, corrected count - 122-147: 4 (125,130,132,135,140,145) actually 6, corrected count - 148-173: 5 (150,152,155,160,165,170) actually 6, corrected count - 174-199: 5 (175,180,185,190,200) actually 5 Corrected frequencies: - 18-43: 7 - 44-69: 7 - 70-95: 11 - 96-121: 8 - 122-147: 6 - 148-173: 6 - 174-199: 5 --- 7. **Problem 2:** For 100 observations, find $k$ using Sturges' Rule: $$k = 1 + \log_2(100) \approx 1 + 6.6439 = 7.6439 \approx 8$$ 8. **Histogram with class intervals of 10:** Classes: 1-10, 11-20, 21-30, 31-40, 41-50, 51-60, 61-70, 71-80 9. **Frequency count:** - 1-10: 9 (1,5,7,10) - 11-20: 6 (12,14,17,19,20) - 21-30: 6 (23,25,27,29,30) - 31-40: 3 (33,35,37) - 41-50: 4 (40,42,45,47,50) - 51-60: 3 (53,55,58,60) - 61-70: 4 (62,65,67,70) - 71-80: 0 Corrected counts: - 1-10: 4 - 11-20: 5 - 21-30: 6 - 31-40: 3 - 41-50: 5 - 51-60: 4 - 61-70: 4 - 71-80: 0 --- 10. **Problem 3:** Create a bar chart for number of students in departments: - Mathematics: 120 - Physics: 80 - Chemistry: 100 - Biology: 90 - Computer Science: 110 --- **Final answers:** - Problem 1: $k=7$, class width $=26$, frequency table as above. - Problem 2: $k=8$, class intervals of 10, frequency counts as above. - Problem 3: Bar chart data as above.