1. **Problem Statement:** We have marks of 50 students in MTH 232 final exams. We need to construct a frequency table and draw a cumulative frequency curve. 2. **Step A: Construct Frequency Table** - First, group the marks into class intervals (e.g., 30-39, 40-49, 50-59, etc.). - Count how many marks fall into each interval. 3. **Class Intervals and Frequencies:** - 30-39: 5 - 40-49: 9 - 50-59: 7 - 60-69: 6 - 70-79: 6 - 80-89: 5 - 90-99: 6 4. **Step B: Cumulative Frequency** - Calculate cumulative frequency by adding frequencies from the first interval up to the current one. 5. **Cumulative Frequencies:** - 30-39: 5 - 40-49: 5 + 9 = 14 - 50-59: 14 + 7 = 21 - 60-69: 21 + 6 = 27 - 70-79: 27 + 6 = 33 - 80-89: 33 + 5 = 38 - 90-99: 38 + 6 = 44 6. **Plotting Cumulative Frequency Curve:** - On x-axis, mark upper class boundaries: 39, 49, 59, 69, 79, 89, 99. - On y-axis, plot cumulative frequencies: 5, 14, 21, 27, 33, 38, 44. - Connect points smoothly to form the ogive (cumulative frequency curve). This curve helps visualize how many students scored below a certain mark. Final frequency table: | Class Interval | Frequency | Cumulative Frequency | |----------------|-----------|----------------------| | 30 - 39 | 5 | 5 | | 40 - 49 | 9 | 14 | | 50 - 59 | 7 | 21 | | 60 - 69 | 6 | 27 | | 70 - 79 | 6 | 33 | | 80 - 89 | 5 | 38 | | 90 - 99 | 6 | 44 |