Question: The following shows the distribution of marks of students in an examination.
6 43 26 18 27
42 8 22 31 39
55 44 37 47 59
10 12 36 53 48
i. Make a stem-and-leaf plot of the marks above
ii. Find the probability of selecting a student who scored between 40 and 50.
iii. Find the number of students who passed the examination, if the pass mark was 30.
1. **State the problem:**
We have a list of student marks and need to:
i. Create a stem-and-leaf plot.
ii. Find the probability of selecting a student scoring between 40 and 50.
iii. Find the number of students who passed if the pass mark is 30.
2. **Stem-and-leaf plot:**
- The stem represents the tens digit.
- The leaf represents the units digit.
Marks: 6, 43, 26, 18, 27, 42, 8, 22, 31, 39, 55, 44, 37, 47, 59, 10, 12, 36, 53, 48
Stem | Leaf
0 | 6, 8
1 | 0, 2, 8
2 | 2, 6, 7
3 | 1, 6, 7, 9
4 | 2, 3, 4, 7, 8
5 | 3, 5, 9
3. **Probability of scoring between 40 and 50:**
- Count marks between 40 and 50 inclusive: 42, 43, 44, 47, 48
- Number of such marks = 5
- Total number of marks = 20
- Probability = $\frac{5}{20} = \frac{\cancel{5}^1}{\cancel{20}^4} = \frac{1}{4}$
4. **Number of students who passed (pass mark 30):**
- Marks 30 or above: 31, 36, 37, 39, 42, 43, 44, 47, 48, 53, 55, 59
- Count = 12
**Final answers:**
- Stem-and-leaf plot as above.
- Probability of scoring between 40 and 50 is $\frac{1}{4}$.
- Number of students who passed = 12.