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.