1. **Problem 8.4.1 and 8.4.2:** Identify the solids in Figure 1 and Figure 2. Since the figures are not provided, typical solids named in such questions are common geometric solids like cube, cuboid, cylinder, cone, sphere, pyramid, or prism. 2. **Problem 8.4.3 and 8.4.4:** Write down the number of faces for the solid in Figure 1 and the number of edges for the solid in Figure 2. - Faces are the flat surfaces of a solid. - Edges are the line segments where two faces meet. 3. **Problem 9.1:** Draw a stem-and-leaf display for the heights. - Stem-and-leaf plots organize data to show distribution. - The stem represents the tens digit, the leaf the units digit. Heights data: 160,170,156,151,165,168,166,163,155,180,164,170,162,160,177,171,182,168,158,160,168,165,152,150,178,181,162,175,174,172,161,173,172,165,162,160,164,166,165,169 Stem | Leaf 150 | 0 1 2 5 6 8 160 | 0 0 0 1 2 2 3 4 4 5 5 5 6 6 8 8 9 170 | 0 0 1 2 2 3 4 5 7 8 180 | 0 1 2 4. **Problem 9.2:** Complete a frequency table for the heights. Group heights by intervals (e.g., 150-154, 155-159, etc.) and count frequencies. | Height Range | Frequency | |--------------|-----------| | 150-154 | 4 | | 155-159 | 4 | | 160-164 | 11 | | 165-169 | 9 | | 170-174 | 7 | | 175-179 | 3 | | 180-184 | 2 | 5. **Problem 9.3:** Calculate the mean height. Mean formula: $$\text{Mean} = \frac{\sum \text{heights}}{\text{number of learners}}$$ Sum of heights = 160+170+156+151+165+168+166+163+155+180+164+170+162+160+177+171+182+168+158+160+168+165+152+150+178+181+162+175+174+172+161+173+172+165+162+160+164+166+165+169 = 6600 Number of learners = 40 Mean = $$\frac{6600}{40} = 165$$ 6. **Problem 9.4:** Find the median height. - Arrange data in ascending order. - Median is the middle value; for even number of data, average the two middle values. Sorted data median position: $$\frac{40}{2} = 20$$ and 21st values. 20th value = 165, 21st value = 165 Median = $$\frac{165 + 165}{2} = 165$$ 7. **Problem 9.5:** Find the mode height. - Mode is the most frequently occurring value. From data, 165 appears most frequently. **Final answers:** - 8.4.1: Name of solid in Figure 1 (depends on figure) - 8.4.2: Name of solid in Figure 2 (depends on figure) - 8.4.3: Number of faces in Figure 1 solid (depends on figure) - 8.4.4: Number of edges in Figure 2 solid (depends on figure) - 9.1: Stem-and-leaf display as above - 9.2: Frequency table as above - 9.3: Mean = 165 - 9.4: Median = 165 - 9.5: Mode = 165