Following is the distribution of marks in Statistics obtained by 32 students :
`{:("Mid - value",5,15,25,35,45,55),("Frequency",4,6,10,7,3,2):}`
Caculate the median marks.

Explanation

Since , we are given the mid - values , we should first find out the upper and limits of the various classes . As the mid - values are 5,15,25,35,45,55,so , class size is 10 (=15-5) . For determining limits of different classes , applying the formula :
Lower limit : `l_(1)=m-(1)/(2)xxi`and
Upper limit : `l_(2)=m+(1)/(2)xxi`
where , i = difference between two mid - values.
In this case, the upper and the lower limits of the first mid - value are :
`l_(1)=5-(1)/(2)xx10=0andl_(2)=5+(1)/(2)xx10=10`
i.e., 0-10 class interval.
Similarly , class intervals for other mid - values are obtained as :

M= Size of `((N)/(2))`th item
= Size of `((32)/(2))` th item= Size of 25th item
Hence, median lies in the class 20-30.
`M=l_(1)+(N/(2)-c.f.)/(f)xxi`
`=20+(32/(2)-10)/(10)xx10`
`=20+(16-10)/(10)xx10`
`=20+(6)/(10)xx10`
`=20+6=26`
Median Marks =26.