Sunflower Heights
1. **State the problem:** We have the heights of 25 sunflower plants shown in a stem-and-leaf diagram. We need to find:
(a) The median height of the plants.
(b) The percentage of plants taller than the average height of 1.9 metres (190 cm).
2. **List all heights in order:**
From the stem-and-leaf:
- 154, 158
- 163, 164, 165, 165
- 172, 172, 173, 176, 176
- 180, 181, 182, 183, 187, 188, 189
- 190, 196, 196
- 203, 204, 204
3. **Find the median height:**
There are 25 plants, so the median is the height of the $\frac{25+1}{2} = 13^{th}$ plant when ordered.
Counting the plants:
- 1 to 2: 154, 158
- 3 to 6: 163, 164, 165, 165
- 7 to 11: 172, 172, 173, 176, 176
- 12 to 18: 180, 181, 182, 183, 187, 188, 189
The 13th plant is the second number in the 12 to 18 range, which is 181 cm.
So, median height = 181 cm.
4. **Calculate percentage taller than 190 cm:**
Plants taller than 190 cm are those with heights > 190 cm:
- 196, 196, 203, 204, 204
Count = 5 plants.
Percentage = $\frac{5}{25} \times 100 = 20$%.
**Final answers:**
(a) Median height = 181 cm
(b) Percentage taller than 190 cm = 20 %