https://file.aiquickdraw.com/mathbot/file/17300626818937bmjcgic.jpg

Let's address each question based on the cumulative frequency graph provided.

### Part (a): Range of Heights
The **range** of the heights can be found by identifying the maximum and minimum heights on the graph.

- From the graph, the **maximum height** appears to be around 55 cm.
- The **minimum height** appears to be 0 cm.

So, the **range of heights** is:
\[
\text{Range} = \text{Maximum height} - \text{Minimum height} = 55 \, \text{cm} - 0 \, \text{cm} = 55 \, \text{cm}
\]

### Part (b): Percentage of Plants Taller Than 45 cm
To find the percentage of plants taller than 45 cm, we need to determine:
1. The cumulative frequency at 45 cm.
2. Subtract this value from the total (80) to get the number of plants taller than 45 cm.
3. Calculate the percentage.

- At 45 cm, the cumulative frequency is approximately 70.
- This means 80 - 70 = 10 plants are taller than 45 cm.

To find the percentage:
\[
\text{Percentage} = \left( \frac{10}{80} \right) \times 100 = 12.5\%
\]

### Final Answers
- **(a)** The range of heights is **55 cm**.
- **(b)** **12.5%** of the plants are taller than 45 cm.

Would you like further details or have any questions?

#### Related Questions
1. How would you find the median height of the plants using the cumulative frequency graph?
2. What is the interquartile range of the heights, and how would you calculate it from the graph?
3. How many plants are shorter than 20 cm, based on the graph?
4. If the distribution is skewed, which direction is it skewed towards?
5. How would you estimate the mean height if you had the actual heights instead of cumulative frequencies?

#### Tip
In cumulative frequency graphs, the total frequency is usually the highest point on the curve, which represents the total number of items in the dataset.

a) What is the range of heights?
b) What percentage of the plants were taller than 45 cm?

Learn how to find the range of heights and the percentage of plants taller than 45 cm using a cumulative frequency graph. This problem covers essential concepts in statistics, including range calculation and percentage determination, suitable for Grades 7-9.

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