Calculate the mean deviation about the median for the following data :

Explanation

Converting the given series into an exclusive series, we prepare the table, given below :

Thus N=100 and therefore, `(N)/(2)=50`
`rArr" median class is 35.5-40.5`
`rArr" "L=35.5, f=26, h=5 and c=37.`
`therefore" median"=L+(((N)/(2)-c))/(f)xxh`
`={35.5+((50-37))/(26)xx5}=(35.5+2.5)=38.`
Thus, M=38.
Now, we prepare the table given below :

Thus, `Sigmaf_(i)xx|x_(i)-M|=735 and N=100.`
`therefore" "MD(M)=(Sigmaf_(i)xx|x_(i)-M|)/(N)=(735)/(100)=7.35.`
Hence, the mean deviation about the median is 7.35.