Use The Given Minimum And Maximum Data Entries

Use The Given Minimum And Maximum Data Entries, And The Minimum = 8, Maximum = 84,6 Classes – The Class Width Is 13

Choose The Correct Lower Class Limits Below.

A. 8, 20, 34, 46, 59, 73
B. 21, 33, 47, 60, 73, 85
C. 8, 21, 34, 47, 60, 73
D. 20, 33, 47, 59, 72, 85
Choose The Correct Upper Class Limits Below.

A. 21, 34, 46, 59, 73, 85
B. 20, 33, 46, 59

The correct answer and explanation is :

Given Data:

• Minimum Value = 8
• Maximum Value = 84
• Number of Classes = 6
• Class Width = 13

Step 1: Calculate the Lower Class Limits

The lower class limits for a grouped frequency distribution are determined by starting at the given minimum value (8) and then adding the class width (13) successively to each lower class limit.

1. First lower class limit: 8 (given as the minimum value)
2. Second lower class limit: 8 + 13 = 21
3. Third lower class limit: 21 + 13 = 34
4. Fourth lower class limit: 34 + 13 = 47
5. Fifth lower class limit: 47 + 13 = 60
6. Sixth lower class limit: 60 + 13 = 73

Thus, the lower class limits are: 8, 21, 34, 47, 60, 73.

Step 2: Calculate the Upper Class Limits

To find the upper class limits, we can add the class width minus 1 (since the interval includes the lower limit and the class width spans the whole range) to each lower class limit.

1. First upper class limit: 8 + 13 – 1 = 20
2. Second upper class limit: 21 + 13 – 1 = 33
3. Third upper class limit: 34 + 13 – 1 = 46
4. Fourth upper class limit: 47 + 13 – 1 = 59
5. Fifth upper class limit: 60 + 13 – 1 = 72
6. Sixth upper class limit: 73 + 13 – 1 = 85

Thus, the upper class limits are: 20, 33, 46, 59, 72, 85.

Step 3: Match to the Given Options

Lower Class Limits:

• The calculated lower class limits are: 8, 21, 34, 47, 60, 73.
• Option C provides these exact values, so the correct answer is C.

Upper Class Limits:

• The calculated upper class limits are: 20, 33, 46, 59, 72, 85.
• Option B provides these exact values, so the correct answer is B.

Final Answer:

• Lower Class Limits: C. 8, 21, 34, 47, 60, 73
• Upper Class Limits: B. 20, 33, 46, 59, 72, 85

Explanation:

• Class Width: The class width is 13, so the difference between the upper and lower class limits of each class should be 13.
• Lower Class Limits: Starting with the given minimum value of 8, we add 13 to each subsequent lower class limit to get the next one.
• Upper Class Limits: To find the upper class limits, we take the lower class limit of each class and add the class width minus 1 (since the lower class limit is included in the interval). This ensures the range for each class is 13.