Calculating Central Angle for Marks 30-40 in a Pie Chart

The problem asks us to find the central angle corresponding to the class interval 30-40 when a pie chart is constructed using the given frequency distribution table, assuming the value of x is 25.

First, let's look at the provided frequency distribution table showing the number of students in different class intervals:

We are given that the value of x is 25. So, the number of students in the 20-30 class interval is 25.

To draw a pie chart, we first need to find the total number of students. We sum up the number of students from all class intervals:

Total number of students = (Number of students in 0-10) + (Number of students in 10-20) + (Number of students in 20-30) + (Number of students in 30-40) + (Number of students in 40-50)

Total number of students = $10 + 15 + 25 + 35 + 15$

Total number of students = $100$

Now, we need to find the central angle for the class interval 30-40. The number of students in this interval is 35. The formula to calculate the central angle for a category in a pie chart is:

Central Angle = $\left(\frac{\text{Frequency of the category}}{\text{Total frequency}}\right) \times 360^\circ$

In this case, the category is the class interval 30-40, and its frequency is the number of students in this interval, which is 35. The total frequency is the total number of students, which is 100.

So, the central angle for the class interval 30-40 is:

Central Angle (30-40) = $\left(\frac{35}{100}\right) \times 360^\circ$

Let's calculate this value:

Central Angle (30-40) = $\frac{35}{100} \times 360^\circ$

Central Angle (30-40) = $\frac{35 \times 360}{100}^\circ$

Central Angle (30-40) = $\frac{35 \times 36}{10}^\circ$

Central Angle (30-40) = $\frac{1260}{10}^\circ$

Central Angle (30-40) = $126^\circ$

Thus, the central angle for the field showing the number of students who got marks in the interval 30-40 is $126^\circ$. This matches option 2.