For the following data set find the upper class boundary 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 **upper class boundary** of the first class, follow these steps:

### Step 1: Identify the Range of the Data
- Find the **minimum** and **maximum** values of the data set.

The data set is:  
2114, 2468, 7119, 1876, 4105, 3183, 1932, 1355, 4278, 2000, 1077, 5835, 1512, 1697, 2478, 3981, 1643, 1858, 1500, 4608, 1000.

- Minimum value = **1000**
- Maximum value = **7119**

### Step 2: Calculate the Range
The **range** is the difference between the maximum and minimum values:

\[
\text{Range} = 7119 - 1000 = 6119
\]

### Step 3: Determine the Number of Classes
You are asked to use **six classes**.

### Step 4: Calculate Class Width
The **class width** is determined by dividing the range by the number of classes, and rounding up if necessary:

\[
\text{Class width} = \frac{\text{Range}}{\text{Number of classes}} = \frac{6119}{6} \approx 1019.83 \approx 1020
\]

### Step 5: Define the First Class
The **lower boundary** of the first class is the minimum value in the data set, which is 1000. The **upper boundary** of the first class is calculated by adding the class width to the lower boundary:

\[
\text{Upper boundary of first class} = 1000 + 1020 = 2020
\]

### Step 6: Upper Class Boundary of First Class
Since the class width is 1020, the upper boundary is calculated as 2020. To account for continuous data, we slightly adjust this value (for example by adding 0.5) to avoid gaps between classes, leading to an **upper class boundary** of:

\[
\text{Upper class boundary} = 2020 + 0.5 = 2020.5
\]

Thus, the **upper class boundary** of the first class is **2020.5**.

Would you like more details on class intervals or any other part? 

Here are 5 related questions for further exploration:
1. How do you find the lower class boundary for the second class?
2. How do you calculate the midpoint of each class?
3. What is the cumulative frequency for this data set?
4. How do you construct a histogram for this data?
5. How do you determine if this data set is skewed?

**Tip:** When rounding class widths, always round up to ensure all data points are covered within the class intervals.

For the following data set find the upper class boundary 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.

Learn how to find the upper class boundary of the first class for a data set representing sales in July. Using key statistical methods, we cover calculating the range, class width, and class boundaries. Suitable for high school students studying data distribution and statistics.

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