NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.3Question 4
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.3
Question. 4
4. Pages written by Sarika in 30 days:
| Pages/day | 16–18 | 19–21 | 22–24 | 25–27 | 28–30 |
|---|---|---|---|---|---|
| Number of days | 1 | 3 | 4 | 9 | 13 |
Find the mean number of pages per day.
Answer:
26 pages/day
Detailed Answer with Explanation:
Step 1: Write class intervals and their frequencies
Class intervals (pages/day): 16–18, 19–21, 22–24, 25–27, 28–30
Number of days (frequency, f): 1, 3, 4, 9, 13
Step 2: Find the mid-point (x) of each class interval
- (16 + 18) ÷ 2 = 17
- (19 + 21) ÷ 2 = 20
- (22 + 24) ÷ 2 = 23
- (25 + 27) ÷ 2 = 26
- (28 + 30) ÷ 2 = 29
So mid-points are: 17, 20, 23, 26, 29
Step 3: Multiply frequency (f) by mid-point (x)
| Class Interval | f | x | f × x |
|---|---|---|---|
| 16–18 | 1 | 17 | 17 |
| 19–21 | 3 | 20 | 60 |
| 22–24 | 4 | 23 | 92 |
| 25–27 | 9 | 26 | 234 |
| 28–30 | 13 | 29 | 377 |
Step 4: Find totals
Σf = 1 + 3 + 4 + 9 + 13 = 30
Σ(f × x) = 17 + 60 + 92 + 234 + 377 = 780
Step 5: Apply mean formula
Mean = Σ(f × x) ÷ Σf
= 780 ÷ 30
= 26 pages/day
Final Answer: 26 pages/day