The table shows the marks scored by a group of students in a class test.
| Marks | 0 | 1 | 2 | 3 | 4 | 5 |
| Frequency | 1 | 4 | 9 | 8 | 5 | 3 |
(a)(i) Calculate the mean mark ; (ii) Find the median.
(b) If the information were to be represented in a pie chart, what would be the sectorial angle for the mark 2?
Explanation
(a)
| x | 0 | 1 | 2 | 3 | 4 | 5 | Total |
| f | 1 | 4 | 9 | 8 | 5 | 3 | 30 |
| fx | 0 | 4 | 18 | 24 | 20 | 15 | 81 |
(i) Mean((bar{x}) = (frac{sum fx}{sum f})
= (frac{81}{30})
= 2.7
(ii) (N = sum f = 30)
(median = frac{1}{2}(N + 1))
= (frac{1}{2}(30 + 1))
=15.5
= The 15th and 16th position.
(therefore median = frac{3 + 3}{2} = 3)
(b) Sectorial angle for the mark 2 = (frac{9}{30} times 360°)
= 108°.