1. **Problem Statement:** We have the time taken (in seconds) by 24 students to solve a problem: 15, 19, 25, 26, 29, 31, 32, 36, 37, 38, 40, 42, 43, 44, 47, 48, 49, 49, 53, 58, 59, 59, 60, 64. We need to: - a) Construct a frequency distribution with class intervals of 10 seconds. - b) Draw a histogram for this distribution. - c) Sketch a frequency polygon on the same graph. 2. **Constructing Frequency Distribution:** - The data ranges from 15 to 64. - Using class intervals of 10 seconds, the classes are: 10-19, 20-29, 30-39, 40-49, 50-59, 60-69. 3. **Counting frequencies:** - 10-19: 15, 19 → 2 - 20-29: 25, 26, 29 → 3 - 30-39: 31, 32, 36, 37, 38 → 5 - 40-49: 40, 42, 43, 44, 47, 48, 49, 49 → 8 - 50-59: 53, 58, 59, 59 → 4 - 60-69: 60, 64 → 2 4. **Frequency distribution table:** | Class Interval | Frequency | |----------------|-----------| | 10 - 19 | 2 | | 20 - 29 | 3 | | 30 - 39 | 5 | | 40 - 49 | 8 | | 50 - 59 | 4 | | 60 - 69 | 2 | 5. **Histogram and Frequency Polygon:** - Histogram bars represent frequencies for each class interval. - Frequency polygon is drawn by joining midpoints of the top of each histogram bar. 6. **Class midpoints:** - 10-19 midpoint: $\frac{10+19}{2} = 14.5$ - 20-29 midpoint: $\frac{20+29}{2} = 24.5$ - 30-39 midpoint: $\frac{30+39}{2} = 34.5$ - 40-49 midpoint: $\frac{40+49}{2} = 44.5$ - 50-59 midpoint: $\frac{50+59}{2} = 54.5$ - 60-69 midpoint: $\frac{60+69}{2} = 64.5$ 7. **Summary:** - Frequency distribution constructed. - Histogram and frequency polygon can be drawn using these frequencies and midpoints.