NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.3Question 7
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.3
Question. 7
7. Weights (kg) of 50 wrestlers:
| Weight (kg) | 100–110 | 110–120 | 120–130 | 130–140 | 140–150 |
|---|---|---|---|---|---|
| No. of wrestlers | 4 | 14 | 21 | 8 | 3 |
Find the mean weight.
Answer:
123.4 kg
Detailed Answer with Explanation:
Step 1: Identify the class intervals and their frequencies.
The weights are divided into groups (called class intervals):
- 100–110 (4 wrestlers)
- 110–120 (14 wrestlers)
- 120–130 (21 wrestlers)
- 130–140 (8 wrestlers)
- 140–150 (3 wrestlers)
Step 2: Find the class marks (midpoints).
For each class interval, the class mark = (lower limit + upper limit) ÷ 2.
- For 100–110: (100 + 110) ÷ 2 = 105
- For 110–120: (110 + 120) ÷ 2 = 115
- For 120–130: (120 + 130) ÷ 2 = 125
- For 130–140: (130 + 140) ÷ 2 = 135
- For 140–150: (140 + 150) ÷ 2 = 145
Step 3: Multiply each frequency (f) with its class mark (x).
| Class Interval (kg) | Class Mark (x) | Frequency (f) | f × x |
|---|---|---|---|
| 100–110 | 105 | 4 | 420 |
| 110–120 | 115 | 14 | 1610 |
| 120–130 | 125 | 21 | 2625 |
| 130–140 | 135 | 8 | 1080 |
| 140–150 | 145 | 3 | 435 |
Step 4: Find the totals.
Total frequency (Σf) = 4 + 14 + 21 + 8 + 3 = 50
Total of f × x (Σfx) = 420 + 1610 + 2625 + 1080 + 435 = 6170
Step 5: Apply the mean formula.
Mean (\(\bar{x}\)) = Σfx ÷ Σf
\(\bar{x} = \dfrac{6170}{50} = 123.4\)
Final Answer: The mean weight of the wrestlers is 123.4 kg.