The table shows the distribution of marks scored by students in a test.
Mark
(%)
10 - 19
20 - 29
30 - 39
40 - 49
50 - 59
60 - 69
70 - 79
80 - 89
90 - 99
Frequency
4
7
12
18
20
14
9
4
2
(a) Construct a cumulative frequency table for the distribution.
(b) Draw a cumulative frequency curve for the distribution.
(c) Use the curve to estimate the:
(i) median;
(ii) probability that a student selected at random obtained distinction, if the lowest mark for distinction is 75%.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a)
Marks
Class
Boundaries
Frequency
Cumulative
Frequency
10 - 19
9.5 - 19.5
4
4
20 - 29
19.5 - 29.5
7
11
30 - 39
29.5 - 39.5
12
23
40 - 49
39.5 - 49.5
18
41
50 - 59
49.5 - 59.5
20
61
60 - 69
59.5 - 69.5
14
75
70 - 79
69.5 - 79.5
9
84
80 - 89
79.5 - 89.5
4
88
90 - 99
89.5 - 99.5
2
90
(b) The cumulative frequency curve
(c)(i) using the curve, the median was 51.5.
(ii) Using the curve, the estimate of tbe number of students who scored at least 75% was 90 - 80 = 10
Therefore, Prob(that a student selected at random obtained distinction) = \(\frac{10}{90} = \frac{1}{9}\)
Source: Myschool Past Questions Archive (Record #56404)