To calculate the class width, we first need to use the following formula:

$\text{Class Width} = \frac{\text{Maximum Value} - \text{Minimum Value}}{\text{Number of Classes}}$

Given the data:

• Minimum = 8
• Maximum = 61
• Number of Classes = 7

Substitute these values into the formula:

$\text{Class Width} = \frac{61 - 8}{7} = \frac{53}{7} \approx 7.57$

So, the class width is approximately 7.57.

Now, let's proceed with the lower class limits and upper class limits:

1. The first lower class limit is the minimum value, which is 8.
2. To find each upper class limit, you add the class width to the previous lower class limit.

The class intervals will be as follows:

• Class 1: Lower limit = 8, Upper limit = $8 + 7.57 \approx 15.57$
• Class 2: Lower limit = 15.57, Upper limit = $15.57 + 7.57 \approx 23.14$
• Class 3: Lower limit = 23.14, Upper limit = $23.14 + 7.57 \approx 30.71$
• Class 4: Lower limit = 30.71, Upper limit = $30.71 + 7.57 \approx 38.28$
• Class 5: Lower limit = 38.28, Upper limit = $38.28 + 7.57 \approx 45.85$
• Class 6: Lower limit = 45.85, Upper limit = $45.85 + 7.57 \approx 53.42$
• Class 7: Lower limit = 53.42, Upper limit = $53.42 + 7.57 \approx 60.99$

Summary:

• Class Width ≈ 7.57
• Lower Class Limits: 8, 15.57, 23.14, 30.71, 38.28, 45.85, 53.42
• Upper Class Limits: 15.57, 23.14, 30.71, 38.28, 45.85, 53.42, 60.99

Would you like further details on how these are derived or have any specific questions?

5 Related Questions:

1. How do you determine the number of classes for a frequency distribution?
2. What is the difference between the class width and class size?
3. How do you handle class limits when the class width is not a whole number?
4. What are class boundaries and how do they differ from class limits?
5. How do you organize data into classes for creating a histogram?

Tip:

When dealing with class widths, round them to a convenient number (e.g., whole numbers) if possible, depending on the context of the problem. This makes interpreting the data easier.