The frequency distribution of marks out of 50 obtained by 50 students in a Mathematics test is partially given below. The frequencies of the second and third classes are missing.
Marks
Frequency
0 – 10
8
10 – 20
a
20 – 30
b
30 – 40
12
40 – 50
6
It is known that:
(i) The total number of students is 50.
(ii) The frequency of the 10 – 20 class is half of that of the 20 – 30 class.
Answer the following:
(a) Determine the missing frequencies a and b.
(b) Construct the cumulative frequency table using the complete set of frequencies.
(c) Identify the median class and calculate the median mark for the test.