| Marks obtained | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| No. of students | 8 | 10 | 22 | 40 | 20 |
Hence determine:
(i) the median
(ii) the pass marks if 85% of the students pass.
(iii) the marks which 45% of the students exceed.
Solution:
Arranging the data in cumulative frequency table.
| Marks obtained | No. of students f | Cumulative frequency |
| 0-10 | 8 | 8 |
| 10-20 | 10 | 18 |
| 20-30 | 22 | 40 |
| 30-40 | 40 | 80 |
| 40-50 | 20 | 100 |
To represent the data in the table graphically, we mark the upper limits of the class intervals on
the horizontal axis (x-axis) and their corresponding cumulative frequencies on the vertical axis ( y-axis).
Plot the points (10, 8), (20, 18), (30, 40), (40, 80), and(50,100) on the graph.
Join the points with the free hand. We get an ogive as shown:
(i) Here number of observations, n = 100 which is even.
So median = ( n/2) th term
= (100/2) th term
= 50 th term
Mark a point A(50) on Y-axis. From A, draw a horizontal line parallel to X-axis meeting the curve at P. From P, draw a line perpendicular to the x-axis which meets it at Q.
Q is the median .
Q = 32.5
Hence the median is 32.5 .
(ii)Total number of students = 100
85% of 100 = 85
Remaining number of students = 100-85 = 15
Mark a point B(15) on Y axis. From B, draw a horizontal line parallel to X-axis meeting the curve at L. From L, draw a line perpendicular to the x-axis which meets it at M.
Here M = 18
The pass marks will be 18 if 85% of students passed.
(iii) Total number of students = 100
45% of 100 = 45
Remaining number of students = 100-45 = 55
Mark a point C(55) on Y axis. From C, draw a horizontal line parallel to X-axis meeting the curve at E. From E, draw a line perpendicular to the x-axis which meets it at F.
Here F = 34
Hence marks which 45% of students exceeds is 34 marks.