Question

The width of each of nine classes in a frequency distribution is 2.5 and the lower class boundary of the lowest class is 10.6. Which one of the following is the upper class boundary of the highest class?

• A. 35.6
• B. 33.1
• C. 30.6
• D. 28.1

Hint:

For continuous class intervals, the boundaries simply stack up:
\[ \text{Upper Boundary} = \text{Start} + (N \times \text{Width}) \]
This direct calculation avoids listing each interval individually.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
A continuous frequency distribution consists of consecutive, non-overlapping class intervals.
The total range covered by the distribution is equal to the product of the number of classes and the class width.

Step 2: Key Formula or Approach:
The upper boundary of the highest class can be calculated directly as:
\[ \text{Upper Boundary of Highest Class} = \text{Lower Boundary of Lowest Class} + (N \times w) \]
where \(N\) is the total number of classes and \(w\) is the class width.

Step 3: Detailed Explanation:
We are given:
- Number of classes, \(N = 9\)
- Width of each class, \(w = 2.5\)
- Lower boundary of the lowest class, \(L_{\text{start}} = 10.6\)
The total range spanned by all 9 continuous classes is:
\[ \text{Total Range} = N \times w = 9 \times 2.5 = 22.5 \]
To find the upper class boundary of the highest (9th) class, we add this total range to the lower boundary of the first class:
\[ \text{Upper Boundary} = L_{\text{start}} + \text{Total Range} \]
\[ \text{Upper Boundary} = 10.6 + 22.5 = 33.1 \]
We can verify this step-by-step by listing the class boundaries:
- Class 1: \(10.6 \text{ to } 13.1\)
- Class 2: \(13.1 \text{ to } 15.6\)
- Class 3: \(15.6 \text{ to } 18.1\)
- Class 4: \(18.1 \text{ to } 20.6\)
- Class 5: \(20.6 \text{ to } 23.1\)
- Class 6: \(23.1 \text{ to } 25.6\)
- Class 7: \(25.6 \text{ to } 28.1\)
- Class 8: \(28.1 \text{ to } 30.6\)
- Class 9: \(30.6 \text{ to } 33.1\)
The upper boundary of the 9th (highest) class is indeed 33.1.
This matches the second option.

Step 4: Final Answer:
Therefore, the correct option is (B).