https://file.aiquickdraw.com/mathbot/file/1726650134477vtotojq1.jpg

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### Given:
- We have the frequency (H) of visits and the ranges for \( k_i \), which represents the number of zoo visits.
- We are to fill in the class width (\( b_i \)), relative frequency (\( h_i \)), and rectangle height based on the provided information.

### Let's calculate the missing values for the table:

The columns are:
1. **Class width**: Difference between class boundaries.
2. **Relative frequency**: Frequency of each class divided by the total number of responses.
3. **Rectangle height**: The relative frequency divided by class width.

Let me now calculate these values.Here is the completed table based on the given dataHere is the completed table based on the given 

| Class boundaries \(k_i\) | Frequencies \(H_i\) | Class widths \(b_i\) | Relative frequencies \(h_i\) | Rectangle heights \(H_i / b_i\) |
|-------------------------|---------------------|----------------------|-----------------------------|---------------------------------|
| \(0 < x \leq 1\)         | 127                 | 1                    | 0.485                       | 0.485                           |
| \(1 < x \leq 4\)         | 111                 | 3                    | 0.424                       | 0.141                           |
| \(4 < x \leq 9\)         | 24                  | 5                    | 0.092                       | 0.018                           |

If you'd like further clarifications or help with GeoGebra visualizations, let me know!

### Follow-up questions:
1. How do we calculate the median for this data set?
2. What is the mode of the data?
3. How can we interpret the rectangle heights in relation to the histogram?
4. How does the class width affect the histogram's shape?
5. How would we calculate the standard deviation for this data?

### Tip: 
In histograms, rectangle height is often used to standardize the representation of data, especially when class widths differ across the intervals.

Analyze the frequency of zoo visits using statistical methods such as relative frequency, class widths, and histogram visualization. This problem involves calculating key statistical values and creating diagrams using tools like GeoGebra. Suitable for students in Grades 9-12.

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