NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.1Question 8
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.1
Question. 8
For the following distribution:
| Marks | Below 10 | Below 20 | Below 30 | Below 40 | Below 50 | Below 60 |
|---|---|---|---|---|---|---|
| No. of students | 3 | 12 | 27 | 57 | 75 | 80 |
The modal class is
10–20
20–30
30–40
50–60
Detailed Answer with Explanation:
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)