The table below shows the frequency distribution of the marks of 800 candidates in an examination.
Marks
0-9
10-19
20-29
30-39
40-49
50-59
60-69
70-79
80-89
90-99
Freq
10
40
80
140
170
130
100
70
40
20
(a) (i) Construct a cumulative frequency table ; (ii) Draw the Ogive ; (iii) Use your ogive to determine the 50th percentile.
(b) The candidates that scored less than 25% are to be withdrawn from the institution, while those that scored than 75% are to be awarded scholarship. Estimate the number of students that will be retained, but will not enjoy the award.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a)(i)
Marks (%)
Freq
Cum Freq
0 - 9
10
10
10 - 19
40
50
20 - 29
80
130
30 - 39
140
270
40 - 49
170
440
50 - 59
130
570
60 - 69
100
670
70 - 79
70
740
80 - 89
40
780
90 - 99
20
800
(ii)
(iii) From the Ogive, the 50th percentile is 70 marks.
(b) Those who scored below 25% (24% and below) = 85 students
Those who scored 75% and below = 710
\(\therefore\) Those who scored above 75% = 800 - 710 = 90 students
Those to be retained without award = 800 - (85 + 90)
= 800 - 175 = 625 students.
Source: Myschool Past Questions Archive (Record #54719)