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Let's go through the problem step by step.

### (a) Cumulative Frequency Diagram
You are required to draw the cumulative frequency diagram. The table already gives the cumulative frequencies for different height intervals:

| Height (h cm)   | Cumulative Frequency |
|-----------------|----------------------|
| \( h \leq 2 \)  | 4                    |
| \( h \leq 4 \)  | 18                   |
| \( h \leq 6 \)  | 42                   |
| \( h \leq 8 \)  | 60                   |
| \( h \leq 10 \) | 72                   |
| \( h \leq 12 \) | 80                   |

These cumulative frequencies should be plotted against the corresponding height on the x-axis.

#### Steps for the diagram:
1. On the x-axis, label heights from 0 to 12 (with a suitable scale).
2. On the y-axis, label cumulative frequencies from 0 to 80.
3. Plot the points:
   - (2, 4)
   - (4, 18)
   - (6, 42)
   - (8, 60)
   - (10, 72)
   - (12, 80)
4. Connect the points smoothly, using a curve.

### (b) Estimate for the Interquartile Range
To find the interquartile range (IQR), we need the first quartile (Q1) and the third quartile (Q3).

- **Q1 (first quartile)**: This represents the value at 25% of the cumulative frequency. Since the total cumulative frequency is 80, Q1 corresponds to \( 25\% \times 80 = 20 \). From the graph, find the height corresponding to a cumulative frequency of 20.
  
- **Q3 (third quartile)**: This represents the value at 75% of the cumulative frequency. \( 75\% \times 80 = 60 \). From the graph, find the height corresponding to a cumulative frequency of 60.

- **Interquartile Range**: \( IQR = Q3 - Q1 \).

### (c) Finding the value of \( H \)
You are told that 28 plants are taller than \( H \) centimeters. This means the cumulative frequency of plants shorter than or equal to \( H \) is \( 80 - 28 = 52 \). From the graph, find the height corresponding to a cumulative frequency of 52. That value is \( H \).

Would you like a more detailed explanation for any of these parts?

Here are 5 related questions:
1. What is the purpose of a cumulative frequency diagram in data analysis?
2. How can we estimate the median from a cumulative frequency graph?
3. What is the significance of the interquartile range in a dataset?
4. How would you interpret a steep section of a cumulative frequency curve?
5. What other statistical measures can be derived from cumulative frequency data?

**Tip**: Always use a smooth curve when plotting cumulative frequency, as it represents a continuous accumulation of data.

Draw a cumulative frequency diagram, estimate the interquartile range, and solve for H when 28 plants are taller than H centimeters.

Learn how to plot a cumulative frequency diagram, estimate the interquartile range, and solve for H when 28 plants are taller than H centimeters. This problem covers key statistical concepts suitable for students in Grades 8-10.

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