Use the following data of tree heights in a field to find the lower and upper-class boundaries of the first class when using five classes. 

 707271706973696870716771707469687171717269716867737470716968. Separate your answers with a comma.

To find the lower and upper-class boundaries of the first class, follow these steps:

1. **Sort the data** (optional, but helpful for clarity):
   - 67, 67, 68, 68, 68, 69, 69, 69, 70, 70, 70, 70, 70, 70, 70, 71, 71, 71, 71, 71, 71, 71, 71, 72, 72, 73, 73, 74, 74, 74, 74

2. **Determine the range**:
   \[
   \text{Range} = \text{Maximum height} - \text{Minimum height} = 74 - 67 = 7
   \]

3. **Find the class width**:
   \[
   \text{Class width} = \frac{\text{Range}}{\text{Number of classes}} = \frac{7}{5} = 1.4
   \]
   Round the class width to a suitable value. In this case, we can round up to **2** to make the classes easier to work with.

4. **Define the classes**:
   The first class will begin at the minimum value of 67. So, the first class would be from 67 to 69 (based on class width of 2).

5. **Find the lower and upper-class boundaries**:
   - The lower-class boundary of the first class is 66.5 (we subtract 0.5 from the class limit of 67).
   - The upper-class boundary of the first class is 69.5 (we add 0.5 to the class limit of 69).

Thus, the lower and upper-class boundaries of the first class are **66.5, 69.5**.

Would you like more details or have any questions?

Here are 5 related questions to expand on this:

1. How do we determine the number of classes to use?
2. What is the impact of rounding the class width?
3. How do you determine class boundaries for subsequent classes?
4. Can class width be non-integer values, and how does it affect the histogram?
5. What is the difference between class boundaries and class limits?

**Tip**: When rounding the class width, rounding up helps avoid overlaps between classes in frequency distributions.

Use the following data of tree heights in a field to find the lower and upper-class boundaries of the first class when using five classes: 707271706973696870716771707469687171717269716867737470716968. Separate your answers with a comma.

Learn how to find the lower and upper-class boundaries for a dataset of tree heights when dividing the data into five classes. The solution explains key statistical concepts, such as range, class width, and how to calculate boundaries. The dataset used includes values such as 67, 68, and 74, with class boundaries calculated as 66.5 and 69.5.

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