The following table shows the ages of the patients admitted in hospital during a month :

Find the mode and the means of the data given above.Compare and interpret the two measure of central tendency.

Explanation

The given data is an inclusive series.Making it an exclusive sesries , we get
Thus ,A= 40.5 ,h =10 ,`Sigma f_i`=80 `Sigma f_i u_i = -37`
`"Mean", barx = A+{h xx (Sigma f_i u_i)/(Sigma f_i)}`
`= 40.5 +{ 10 xx (-37)/80}= 40.5 -37/8`
`= 40.5 - 4.63 = 35.87` Also , the modal class of the given data is 35.5-45.5, as it has the maximum frequecy
`therefore x_k=35.5, f_k-=23,, f_(k-1)=21, f_(k+1)=14 and h=10`
Mode, `M_0=x_k+{hxx((f_k-f_(k-1)))/((2f_k-f_(k-1)-f_(k+1)))}`
`35.5+{10xx((23-31))/((2xx23-21-14))}=35.5+((10xx2)/(11))`
`=35.5+1.82=37.32` Clearly mode gt mean