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Q.

Draw 'less than ogive' and 'more than ogive' for the following distribution and hence its median is,


Question Image

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a

58.33.

b

59.33.

c

68.33.

d

78.33. 

answer is A.

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Detailed Solution

Given table is,
Question ImageConsider the table
 

Classes

Frequency

Cumulative Frequency

20-30

10

Less than 30

10

More than 20

100

30-40

8

Less than 40

18

More than 30

90

40-50

12

Less than 50

30

More than 40

82

50-60

24

Less than 60

54

More than 50

70

60-70

6

Less than 70

60

More than 60

46

70-80

25

Less than 80

85

More than 70

40

80-90

15

Less than 90

100

More than 80

15

To draw the more than type ogive, we plot 20,100 , 30,90 , 40,82 , 50,70 , 60,46 , 70,40 , 80,15   on the graph and join the points free hand. The graph obtained by this is the required more than type ogive.
To draw the less than type ogive, we plot (30,10) (40,18) (50,30) (60,54), 70,60 , 80,85 , 90,100   on the graph and join the points free hand. The graph obtained by this is the required less than type ogive.
Question ImageWe know that the x-coordinate of the intersection point of two ogives is the median. Here, the x-coordinate of the intersection of the less than type and more than type ogive  is 58.33.
So, the median is 58.33.
Therefore, option 1 is correct.
 
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