The frequency table shows the marks scored by 32 students in a test.
Marks scored
1
2
3
4
5
6
7
8
9
10
No of students
2
3
4
4
4
4
5
3
2
1
Find the :
(a)(i) mean ; (ii) median ; (iii) mode of the marks;
(b) percentage of the students who scored at least 8 marks.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
x
1
2
3
4
5
6
7
8
9
10
Total
f
2
3
4
4
4
4
5
3
2
1
32
fx
2
6
12
16
20
24
35
24
18
10
167
(a)(i) Mean = \(\frac{\sum fx}{\sum f} = \frac{167}{32}\)
= \(5.21875 \approxeq 5.22\)
(ii) By inspection, the average of the numbers in the 16th and 17th position give the median
= \(\frac{5 + 5}{2} = 5\)
(iii) Mode = 7 marks having the largest frequency.
(b) Students who scored at least 8 marks = Those who scored 8, 9, 10.
Total number of students that scored at least 8 = 3 + 2 + 1 = 6.
\(%age = \frac{6}{32} \times 100% = 18.75%\)
Source: Myschool Past Questions Archive (Record #54525)