following table shows the distribution of marks in Mathematics:
Marks (less than) No. of students
10 7
20 28
30 54
40 71
50 84
60 105
70 147
80 180
With the help of a graph paper, taking 2 cm = 10 units along one axis and 2 cm
= 20 units along the other axis, plot an ogive for the above distribution and use
it to find the:
(i) median.
(ii) number of students who scored distinction marks (75% and above)
(iii) number of students, who passed the examination if pass marks is 35%.
Answers
Given : distribution of marks in Mathematics
To Find : plot an ogive , find median , number of students who scored distinction marks (75% and above) , number of students, who passed the examination if pass marks is 35%
Solution:
Marks less than Number of students
10 7
20 28
30 54
40 71
50 84
60 105
70 147
80 180
Less than ogive
The points with the upper limits of the class are plotted on x axis and the corresponding less than cumulative frequencies on y axis.
The points are joined by free hand smooth curve to give less than cumulative frequency curve or the less than Ogive
Median from graph approx = 52
52 Marks
number of students who scored distinction marks (75% and above)
75 % of 80 = 60 and above
= 180 - 105
= 75 Students
75 Students got distinction marks (75% and above)
number of students, who passed the examination if pass marks is 35%.
35 % of 80 = 28
From graph 50
Students passes = 180 - 50 = 130
130 Students passed the examination
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