To determine the appropriate scale and interval for the histogram, let's analyze the given data. Here are the steps:
1. Identify the Range of Data:
- The given ranges are: [tex]$1-10$[/tex], [tex]$11-20$[/tex], [tex]$21-30$[/tex], [tex]$31-40$[/tex], [tex]$41-50$[/tex], [tex]$51-60$[/tex], [tex]$61-70$[/tex], [tex]$71-80$[/tex], [tex]$81-90$[/tex], and [tex]$91-100$[/tex].
2. Identify the Count Values:
- The counts corresponding to the ranges are: 1, 0, 1, 1, 2, 4, 6, 11, 5, and 4.
3. Determine the Data Range:
- The data spans from 0 to 11 based on the counts given for each range.
4. Determine the Suitable Scale:
- The scale must accommodate the highest count value observed in the data, which is 11.
5. Analyze the Options:
- Option 1: The scale should be [tex]$0-10$[/tex], and the interval should be 10.
- This scale does not accommodate the maximum count value of 11, so it is not the best option.
- Option 2: The scale should be [tex]$0-15$[/tex], and the interval should be 5.
- This scale can accommodate the highest count value of 11 and divides the range into suitable intervals.
- Option 3: The scale should be 1-10, and the interval should be 5.
- This scale does not reach up to the maximum count value of 11, making it unsuitable.
- Option 4: The scale should be 1-15, and the interval should be 10.
- This scale covers up to the count of 11, but the interval of 10 is too large and not as informative for smaller ranges.
6. Conclusion:
- Considering the data spans from 0 to 11 and the most appropriate interval for representing the data comprehensively with smaller steps is an interval of 5 within a scale up to 15.
Thus, the most appropriate choice is:
The scale should be [tex]$0-15$[/tex], and the interval should be 5.
