Question

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:

Answer 1

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+(f_1-f_0)/(2f_1-f_0-f_2)**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+(40-24)/(80-24-33)**500 = 1500+16/23**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,`(barX) = a+(sumf_iu_i)/(sumf_i)**h`
Here, `a =` assumed mean `= 2750`
`sumf_iu_i = -35`
`sumf_i = 200`
`h =` = step size `=500`
Putting these values in formula,
`barX = 2750+(-35)**500/200 = 2750-87.5 = 2662.5`