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## Sagot :

**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**