To construct a frequency polygon for the given data, we need to follow these steps:

Step 1: Identify the class intervals and frequencies

From the table:

• Class intervals (Marks): 50–52, 47–49, 44–46, 41–43, 38–40, 35–37, 32–34
• Frequencies (Number of students): 4, 10, 15, 18, 20, 12, 13

Step 2: Determine the class marks

Class marks are calculated using the formula: $\text{Class mark} = \frac{\text{Lower limit} + \text{Upper limit}}{2}$

• For 50–52: $(50 + 52) / 2 = 51$
• For 47–49: $(47 + 49) / 2 = 48$
• For 44–46: $(44 + 46) / 2 = 45$
• For 41–43: $(41 + 43) / 2 = 42$
• For 38–40: $(38 + 40) / 2 = 39$
• For 35–37: $(35 + 37) / 2 = 36$
• For 32–34: $(32 + 34) / 2 = 33$

Step 3: Add boundary points

To close the frequency polygon, add class marks before the first interval and after the last interval with zero frequency:

• Add $\text{Class mark} = 30$ with frequency 0
• Add $\text{Class mark} = 54$ with frequency 0

Step 4: Plot the frequency polygon

The points to plot are:

• (30, 0)
• (33, 13)
• (36, 12)
• (39, 20)
• (42, 18)
• (45, 15)
• (48, 10)
• (51, 4)
• (54, 0)

Step 5: Draw

To create the frequency polygon:

1. Plot the class marks on the x-axis and their corresponding frequencies on the y-axis.
2. Join the points with straight lines.

If you'd like, I can generate this frequency polygon for you. Let me know! 😊

Would you like a graphical representation or any additional clarification?

Related Questions:

1. What is the difference between a histogram and a frequency polygon?
2. How can you use cumulative frequency instead of frequency for such data?
3. How does adding boundary points help close a frequency polygon?
4. Can you explain how to interpret a frequency polygon?
5. What is the significance of the class mark in constructing such graphs?

Tip:

Always ensure to label axes correctly and scale them uniformly for an accurate graphical representation!