NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.3Question 8
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.3
Question. 8
8. Mileage (km/l) of 50 cars:
| Mileage | 10–12 | 12–14 | 14–16 | 16–18 |
|---|---|---|---|---|
| No. of cars | 7 | 12 | 18 | 13 |
Find the mean mileage. The manufacturer claimed the model gave 16 km/litre. Do you agree?
Answer:
14.48 km/l (Claim of 16 km/l is not supported.)
Detailed Answer with Explanation:
Step 1: Identify the data.
- The table shows classes of mileage (in km per litre) and the number of cars in each class.
- Total number of cars = 50.
Step 2: Find the class marks (mid-points).
For each class interval, the class mark = (lower limit + upper limit) ÷ 2.
- For 10–12: (10 + 12) ÷ 2 = 11
- For 12–14: (12 + 14) ÷ 2 = 13
- For 14–16: (14 + 16) ÷ 2 = 15
- For 16–18: (16 + 18) ÷ 2 = 17
Step 3: Multiply class mark with frequency (number of cars).
| Mileage (km/l) | No. of cars (f) | Class mark (x) | f × x |
|---|---|---|---|
| 10–12 | 7 | 11 | 77 |
| 12–14 | 12 | 13 | 156 |
| 14–16 | 18 | 15 | 270 |
| 16–18 | 13 | 17 | 221 |
| Total | 50 | – | 724 |
Step 4: Apply the formula for Mean.
Mean mileage (\( \bar{x} \)) = (Σ f × x) ÷ (Σ f)
= 724 ÷ 50
= 14.48 km/l
Step 5: Compare with manufacturer’s claim.
The manufacturer claimed the mileage = 16 km/l.
But the actual mean mileage = 14.48 km/l.
Conclusion: The claim of 16 km/l is not supported by the data.