Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Get quick and reliable solutions to your questions from a community of experienced experts on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
Sure, let's analyze the given data step by step to find the answers to the questions.
Given Data:
| उमेर वर्षमा (Age in years) | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
|----------------------------|------|-------|-------|-------|-------|
| खेलाडी सङ्या (Number of players) | 6 | 4 | 5 | 4 | 11 |
a) Modal Class of the Given Data:
The modal class is the class interval with the highest frequency. In our data:
- Number of players in 0-10 years: 6
- Number of players in 10-20 years: 4
- Number of players in 20-30 years: 5
- Number of players in 30-40 years: 4
- Number of players in 40-50 years: 11
The highest frequency is 11, which corresponds to the class interval 40-50 years. Therefore, the modal class is:
(40, 50)
b) Median Class of the Given Data:
To find the median class, we need to determine the class interval that contains the median.
- The total number of players: 6 + 4 + 5 + 4 + 11 = 30
- The median position (n/2) = 30/2 = 15
We need to find the class interval where the cumulative frequency reaches or exceeds 15:
1. Cumulative frequency for 0-10 years: 6
2. Cumulative frequency for 10-20 years: 6 + 4 = 10
3. Cumulative frequency for 20-30 years: 10 + 5 = 15
4. Cumulative frequency for 30-40 years: 15 + 4 = 19
5. Cumulative frequency for 40-50 years: 19 + 11 = 30
The cumulative frequency first reaches 15 in the class interval 20-30 years. Therefore, the median class is:
(20, 30)
c) First Quartile (Q1) of the Given Data:
The first quartile (Q1) position is at (n/4) = 30/4 = 7.5
We need to find the class interval where the cumulative frequency reaches or exceeds 7.5:
1. Cumulative frequency for 0-10 years: 6
2. Cumulative frequency for 10-20 years: 6 + 4 = 10
3. Cumulative frequency for 20-30 years: 10 + 5 = 15
4. Cumulative frequency for 30-40 years: 15 + 4 = 19
5. Cumulative frequency for 40-50 years: 19 + 11 = 30
The cumulative frequency first reaches or exceeds 7.5 in the class interval 10-20 years. Therefore, the first quartile (Q1) lies in:
(10, 20)
d) Average Age of Players Under 20 Years:
To find the average age of players under 20 years, we need to consider the players in the class intervals 0-10 and 10-20 years:
- Number of players in 0-10 years: 6
- Number of players in 10-20 years: 4
Total number of players under 20 years = 6 + 4 = 10
We calculate the midpoint (average age within each class interval) and then find the weighted average:
- Midpoint of 0-10 years = (0 + 10) / 2 = 5 years
- Midpoint of 10-20 years = (10 + 20) / 2 = 15 years
Weighted average age:
[tex]\( \text{Average age} = \frac{(6 \times 5) + (4 \times 15)}{6 + 4} \)[/tex]
= [tex]\( \frac{30 + 60}{10} \)[/tex]
= [tex]\( \frac{90}{10} \)[/tex]
= 9 years
Therefore, the average age of players under 20 years is:
9 years
Given Data:
| उमेर वर्षमा (Age in years) | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
|----------------------------|------|-------|-------|-------|-------|
| खेलाडी सङ्या (Number of players) | 6 | 4 | 5 | 4 | 11 |
a) Modal Class of the Given Data:
The modal class is the class interval with the highest frequency. In our data:
- Number of players in 0-10 years: 6
- Number of players in 10-20 years: 4
- Number of players in 20-30 years: 5
- Number of players in 30-40 years: 4
- Number of players in 40-50 years: 11
The highest frequency is 11, which corresponds to the class interval 40-50 years. Therefore, the modal class is:
(40, 50)
b) Median Class of the Given Data:
To find the median class, we need to determine the class interval that contains the median.
- The total number of players: 6 + 4 + 5 + 4 + 11 = 30
- The median position (n/2) = 30/2 = 15
We need to find the class interval where the cumulative frequency reaches or exceeds 15:
1. Cumulative frequency for 0-10 years: 6
2. Cumulative frequency for 10-20 years: 6 + 4 = 10
3. Cumulative frequency for 20-30 years: 10 + 5 = 15
4. Cumulative frequency for 30-40 years: 15 + 4 = 19
5. Cumulative frequency for 40-50 years: 19 + 11 = 30
The cumulative frequency first reaches 15 in the class interval 20-30 years. Therefore, the median class is:
(20, 30)
c) First Quartile (Q1) of the Given Data:
The first quartile (Q1) position is at (n/4) = 30/4 = 7.5
We need to find the class interval where the cumulative frequency reaches or exceeds 7.5:
1. Cumulative frequency for 0-10 years: 6
2. Cumulative frequency for 10-20 years: 6 + 4 = 10
3. Cumulative frequency for 20-30 years: 10 + 5 = 15
4. Cumulative frequency for 30-40 years: 15 + 4 = 19
5. Cumulative frequency for 40-50 years: 19 + 11 = 30
The cumulative frequency first reaches or exceeds 7.5 in the class interval 10-20 years. Therefore, the first quartile (Q1) lies in:
(10, 20)
d) Average Age of Players Under 20 Years:
To find the average age of players under 20 years, we need to consider the players in the class intervals 0-10 and 10-20 years:
- Number of players in 0-10 years: 6
- Number of players in 10-20 years: 4
Total number of players under 20 years = 6 + 4 = 10
We calculate the midpoint (average age within each class interval) and then find the weighted average:
- Midpoint of 0-10 years = (0 + 10) / 2 = 5 years
- Midpoint of 10-20 years = (10 + 20) / 2 = 15 years
Weighted average age:
[tex]\( \text{Average age} = \frac{(6 \times 5) + (4 \times 15)}{6 + 4} \)[/tex]
= [tex]\( \frac{30 + 60}{10} \)[/tex]
= [tex]\( \frac{90}{10} \)[/tex]
= 9 years
Therefore, the average age of players under 20 years is:
9 years
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.
