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.