The mode of the following series is 36 . Find the missing frequency in it

Explanation

Since the mode of the given series is 36 and maximum frequency 16 lies in the class 30-40 , so the modal class is 30-40 . Let the missing frequency be x Then
`therefore x_k=30,f_k=16, f_(k-1)=x, f_(k+1)=12 and h=10`
Also `m_0=36` Using the formula , ` M_o=x_k+{hxx((f_k-f_(k-1)))/(2f_k-f_(k-1)-f_(k+1)}` we get
`30+{10xx((16-x))/((32-x-12))}=36`
`rArr(10xx(160-x))/((20-x))=6 rArr 160-10x=120-6x`
`rArr 4x=40 rArrx=10`
Hence , the missing frequency is 10