For the following data set find the frequency of the first class when using six classes: 

Sales in July in dollars by representatives at a company
2114
    
2468
    
7119
    
1876
    
4105
    
3183
    
1932
    
1355
    
4278
    
2000
    
1077
    
5835
    
1512
   
1697
    
2478
    
3981
    
1643
    
1858
    
1500
    
4608
     
1000
 .

To find the frequency of the first class, we need to follow a few steps for this dataset:

### Step-by-step solution:

1. **Arrange the data in ascending order** (to find the range easily):
   \[
   1000, 1077, 1355, 1500, 1512, 1643, 1697, 1858, 1876, 1932, 2000, 2114, 2468, 2478, 3183, 3981, 4105, 4278, 4608, 5835, 7119
   \]

2. **Determine the range** of the dataset:
   \[
   \text{Range} = \text{Max value} - \text{Min value} = 7119 - 1000 = 6119
   \]

3. **Decide on the number of classes**: 
   You're asked to use 6 classes.

4. **Calculate the class width** using the formula:
   \[
   \text{Class width} = \frac{\text{Range}}{\text{Number of classes}} = \frac{6119}{6} \approx 1019.83 \approx 1020
   \]
   So, the class width will be 1020.

5. **Determine the class boundaries**:
   - First class: \(1000\) to \(2020\)
   - Second class: \(2021\) to \(3040\)
   - Third class: \(3041\) to \(4060\)
   - Fourth class: \(4061\) to \(5080\)
   - Fifth class: \(5081\) to \(6100\)
   - Sixth class: \(6101\) to \(7120\)

6. **Count the frequency of the first class**:
   The first class is from \(1000\) to \(2020\). The values that fall within this range are:
   \[
   1000, 1077, 1355, 1500, 1512, 1643, 1697, 1858, 1876, 1932, 2000
   \]
   There are **11 values** in this class.

### Final Answer:
The frequency of the first class is **11**.

---

Would you like more details or have any questions about this process?  

Here are some related questions:
1. How do you calculate the relative frequency for a class?
2. What is the midpoint of the first class?
3. How would the process change if there were 7 classes instead of 6?
4. How can you construct a frequency histogram for this data set?
5. How can you find the cumulative frequency for each class?

**Tip**: When calculating the class width, always round up to ensure all data points are included.

For the following data set find the frequency of the first class when using six classes: Sales in July in dollars by representatives at a company: 2114, 2468, 7119, 1876, 4105, 3183, 1932, 1355, 4278, 2000, 1077, 5835, 1512, 1697, 2478, 3981, 1643, 1858, 1500, 4608, 1000.

Find the frequency of the first class in a sales data set, grouped into six classes. This solution involves calculating the range, class width, and counting the frequency of data points within the first class interval, suitable for Grades 9-12 students learning about frequency distributions in statistics.

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