### Given Data:
The table represents the ages (in years) of 24 people in a village distributed across different age groups. The age groups and corresponding frequencies are as follows:
| Age Group (years) | Number of People |
|-------------------|------------------|
| 10 - 20 | 2 |
| 20 - 30 | 5 |
| 30 - 40 | 6 |
| 40 - 50 | 3 |
| 50 - 60 | 4 |
| 60 - 70 | 4 |
### (प) What is the modal class in the above table?
The modal class is the class interval with the highest frequency.
- Frequencies: [2, 5, 6, 3, 4, 4]
- Maximum Frequency: 6
The age group corresponding to this maximum frequency is 30 - 40.
The modal class is (30, 40).
### (9) Find the median class. Calculate the median from the given data.
To calculate the median class:
1. Determine the total number of people: [tex]\(24\)[/tex].
2. The median position is at [tex]\(\frac{n}{2}\)[/tex], where [tex]\( n \)[/tex] is the total number of people.
3. Median position: [tex]\( \frac{24}{2} = 12 \)[/tex].
Identify the cumulative frequency until it reaches or exceeds the median position (12).
- Cumulative frequency:
- 2 (10-20)
- 2 + 5 = 7 (20-30)
- 7 + 6 = 13 (30-40)
- Thus, 12 falls into the 30-40 age group.
The median class is (30, 40).
### (घ) Compare in the ratio the number of people whose ages are above and below the median class.
Identify the number of people below and above the median class:
- People in age groups below 30-40:
- (10-20): 2
- (20-30): 5
- Total below: 2 + 5 = 7
- People in age groups above 30-40:
- (40-50): 3
- (50-60): 4
- (60-70): 4
- Total above: 3 + 4 + 4 = 11
Compare the number of people above and below the median class:
- Ratio of people above to below the median class:
[tex]\[
\text{Ratio} = \frac{\text{People above}}{\text{People below}} = \frac{11}{7} \approx 1.571
\][/tex]
The ratio of people above to below the median class is approximately 1.571.
