Question

For the following distribution, the modal class is :

• A. 10-20
• B. 20-30
• C. 30-40
• D. 50-60

Hint:

To find the modal class from a cumulative table quickly, look for the largest difference between consecutive cumulative frequency values.
The jump from 27 to 57 is 30, which is the largest increase in the list.
This corresponds directly to the interval 20-30.

Answer 1

The Correct Option is B

Step 1: Recall what a modal class means.
Once we turn the cumulative data into ordinary class frequencies, the modal class is simply the one with the tallest bar, the highest frequency.
Step 2: Peel off the frequencies working from the top of the table downward.
The cumulative values given are Below 10 = 12, Below 20 = 27, Below 30 = 57, Below 40 = 75, Below 50 = 80. Working down from the top: \[ (40\text{-}50) = 80 - 75 = 5 \] \[ (30\text{-}40) = 75 - 57 = 18 \] \[ (20\text{-}30) = 57 - 27 = 30 \] \[ (10\text{-}20) = 27 - 12 = 15 \] and the first class $(0\text{-}10)$ keeps its own value, 12.
Step 3: Compare all five frequencies.
We now have 12, 15, 30, 18, 5 for the five classes in order. The largest by far is 30.
Step 4: Conclude. \[ \boxed{20\text{-}30} \]