Calculate median of the following data :
`{:("Marks",46-50,41-45,36-40,31-35,36-30,21-25,16-20,11-15),("Number of Students"," "5," "11," "22," "35," " 26," "13," "10," "7):}`

Explanation

This is an inclusive series given in the descending order . It should first be converted into an exclusive series and placed in the ascending order, as in the following table :

Median , M = Size of `((N)/(2))` th item , N= `sumf=129`
= Size of `((129)/(2))` th item
= Size of 64.5 th item
64.5th item lies in 91 st cumulative frequency of the series . The corresponding class interval , 30.5-35.5, would therefore , be the Median class interval.
Using the foormula, `M=l_(1)+(N/(2)-c.f.)/(f)xxi`
`=30.5+(129/(2)-56)/(35)xx5`
`30.5+(64.5-56)/(35)xx5=30.5+(8.5)/(35)xx5`
`=30.5+1.2=31.7`
Median = 31.7 marks.