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Determine median value of the following ...

Determine median value of the following series using graphic method :
`{:("Marks",0-5,5-10,10-15,15-20,20-25,25-30,30-35,35-40),("Number of students"," "4," "6," "10," "10," "22," "25," "18," "5):}`

Text Solution

Verified by Experts

Using 'Less then ogive approach , the calculation of the median value involves the following steps :
(i) concert the series into a less than cumulative frequency distribution and graph the data as under :

(ii) Find out `((N)/(2))` th item and mark it on the Y-axis . In the above illustration `((N)/(2))` th item is `(100)/(2)=50`.
(iii) Draw a perpendicular from 50 to the right to cut the cumulative point E where cumulative frequency curve (ogive) at point E.
(iv) From the point E where cumulative frequency curve (ogive) is cut , draw a perpendicular on X- axis . The point at which it touches X- axis will be the median value if the series ,as shown in Graph A :

Using 'more' than ogive approach , the calculation of the median involves the similar procedure , as should be evident from the following table and Graph B :

Median = 24

Median = 24
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