NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.3Question 2
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.3
Question. 2
2. Calculate the mean of the scores of 20 students in a mathematics test :
| Marks | 10–20 | 20–30 | 30–40 | 40–50 | 50–60 |
|---|---|---|---|---|---|
| Number of students | 2 | 4 | 7 | 6 | 1 |
Answer:
35
Detailed Answer with Explanation:
Step 1: Write down the class intervals and frequencies.
We are given:
- Marks (class intervals): 10–20, 20–30, 30–40, 40–50, 50–60
- Number of students (frequency, f): 2, 4, 7, 6, 1
Step 2: Find the class marks (x).
Class mark = (lower limit + upper limit) ÷ 2
- For 10–20: (10 + 20) ÷ 2 = 15
- For 20–30: (20 + 30) ÷ 2 = 25
- For 30–40: (30 + 40) ÷ 2 = 35
- For 40–50: (40 + 50) ÷ 2 = 45
- For 50–60: (50 + 60) ÷ 2 = 55
So, class marks are: 15, 25, 35, 45, 55.
Step 3: Multiply frequency (f) with class mark (x).
| Class interval | f | x | f × x |
|---|---|---|---|
| 10–20 | 2 | 15 | 30 |
| 20–30 | 4 | 25 | 100 |
| 30–40 | 7 | 35 | 245 |
| 40–50 | 6 | 45 | 270 |
| 50–60 | 1 | 55 | 55 |
Step 4: Add the totals.
- Total of frequencies, \(\sum f = 2 + 4 + 7 + 6 + 1 = 20\)
- Total of f × x, \(\sum f x = 30 + 100 + 245 + 270 + 55 = 700\)
Step 5: Apply the formula of mean.
Mean, \(\bar{x} = \dfrac{\sum f x}{\sum f}\)
\(\bar{x} = \dfrac{700}{20} = 35\)
Final Answer: The mean marks = 35.