| Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 |
| No. of students | 5 | 9 | 16 | 22 | 26 | 18 | 11 | 6 | 4 | 3 |
Draw an ogive for the given distribution on a graph sheet. Use a suitable scale for ogive to estimate the following:
(i) the median
(ii) the lower quartile
(iii) the number of students who obtained more than 75% marks in the test.
(iv) the number of students who did not pass in the test if the pass percentage was 40. (2002)
Solution:
We write the given data in cumulative frequency table.
| Marks | No. of students | Cumulative frequency c.f |
| 0-10 | 5 | 5 |
| 10-20 | 9 | 14 |
| 20-30 | 16 | 30 |
| 30-40 | 22 | 52 |
| 40-50 | 26 | 78 |
| 50-60 | 18 | 96 |
| 60-70 | 11 | 107 |
| 70-80 | 6 | 113 |
| 80-90 | 4 | 117 |
| 90-100 | 3 | 120 |
Plot the points (10, 5), (20, 14), (30, 30), (40, 52), (50, 78), (60, 96), (70, 107), (80, 113), (90, 117) and (100, 120) on the graph.
Join the points with the free hand. We get an ogive as shown:
(i)Here n = 120
Median = (n/2)th term
= 120/2
= 60th term
Mark point A(60) on Y axis. Draw a line parallel to X axis from A.
Let it meet the curve at B. Draw a straight line from B to X axis which meets at C.
C = 50
Hence median is 50.
(ii)Lower quartile = (n/4)th term
= 120/4
= 30th term
Mark a point P (30) on Y axis. Draw a line parallel to X axis from that point.
Let it meet the curve at Q. From that point draw a perpendicular which meets X axis at R.
The point R is 30.
Hence lower quartile is 30.
(iii)Mark a point U(75) on X axis.
Draw a line parallel to Y axis which meets curve at T.
From T, draw a line parallel to X axis to meet Y axis at S.
S = 110
No. of students who obtained more than 75% = 120-110 = 10
(iv) Mark a point Z(40) on X axis.
Draw a line parallel to Y axis which meets curve at Y.
From Y, draw a line parallel to X axis to meet Y axis at X.
X = 52
No of students who failed if 40% is the pass percentage is 52.