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.
Explanation
| 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.
\(%age = \frac{6}{32} \times 100% = 18.75%\)