The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure:

Solution: Here, Maximum frequency is $40$.
So, Modal class will be corresponding class to $40$ that is , $1500-2000$.
Now, Mode can be given by formula,
$Mode=l+\frac{f_1-f_0}{2f_1-f_0-f_2}\ast h$
Here, $l=$ Lower limit of modal class $=1500$
$f_1=$ Frequency of Modal class $=40$
$f_2=$ Frequency of Pre Modal class $=24$
$f_3=$ Frequency of Succeeding Modal class $=33$
$h=$ Class interval $=500$
Putting these values in Mode formula,
$Mode=1500+\frac{40-24}{80-24-33}\ast 500=1500+\frac{16}{23}\ast 500=1500+347.82=1847.82$

Now, we will calculate mean for the given data.
Here, we can use step deviation method to find the mean of given data.
First we have to construct a table for the given data. Please refer to video for creating complete table.
We know, Mean,$\left(\overline{X}\right)=a+\frac{\sum f_i{u}_i}{\sum f_i}\ast h$
Here, $a=$ assumed mean $=2750$
$\sum f_i{u}_i=-35$
$\sum f_i=200$
$h=$ = step size $=500$
Putting these values in formula,
$\overline{X}=2750+\left(-35\right)\ast \frac{500}{200}=2750-87.5=2662.5$