For the following distribution, the modal class is :
Show 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.
Step 1: Understanding the Question:
This question is from Statistics, focusing on grouped data analysis.
We are given a cumulative frequency table of the "less than" type. We need to convert it into a standard frequency table to find the modal class.
Step 2: Key Formula or Approach:
The modal class is the class interval that has the highest individual frequency.
Since the table lists cumulative frequencies ("Below 10", "Below 20", etc.), we must subtract consecutive cumulative values to find the actual frequency of each interval.
Step 3: Detailed Explanation:
The given cumulative frequency table is:
- Below 10: 12
- Below 20: 27
- Below 30: 57
- Below 40: 75
- Below 50: 80
Let us construct the frequency table for each interval:
1. Class 0-10:
\[ \text{Frequency} = 12 \]
2. Class 10-20:
\[ \text{Frequency} = (\text{Below 20}) - (\text{Below 10}) = 27 - 12 = 15 \]
3. Class 20-30:
\[ \text{Frequency} = (\text{Below 30}) - (\text{Below 20}) = 57 - 27 = 30 \]
4. Class 30-40:
\[ \text{Frequency} = (\text{Below 40}) - (\text{Below 30}) = 75 - 57 = 18 \]
5. Class 40-50:
\[ \text{Frequency} = (\text{Below 50}) - (\text{Below 40}) = 80 - 75 = 5 \]
Comparing the frequencies of the class intervals:
- 0-10: 12
- 10-20: 15
- 20-30: 30
- 30-40: 18
- 40-50: 5
The highest frequency is 30, which belongs to the class interval 20-30.
Therefore, the modal class is 20-30.
