NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.1

Question 8

Step 1: Understand the table

The given data is in the form of cumulative frequencies (students below 10, below 20, etc.). To find the modal class, we first need to convert it into class frequencies.

Step 2: Find class frequencies

We subtract each cumulative value from the previous one:

• Below 10 → 3 (no subtraction needed)
• 10–20 → 12 – 3 = 9
• 20–30 → 27 – 12 = 15
• 30–40 → 57 – 27 = 30
• 40–50 → 75 – 57 = 18
• 50–60 → 80 – 75 = 5

So the class frequencies are: 3, 9, 15, 30, 18, 5.

Step 3: Identify the highest frequency

The frequencies are 3, 9, 15, 30, 18, and 5. The largest number is 30.

Step 4: Find the class interval with this highest frequency

The frequency 30 belongs to the class 30–40.

Step 5: Write the conclusion

The class with the highest frequency is called the modal class. Therefore, the modal class is 30–40.

Final Answer: Option C (30–40)