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?
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(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 = \(\frac{9}{30} \times 360^\circ\)
= 108^\circ.
Source: Myschool Past Questions Archive (Record #53139)