Question

The following data gives the distribution of total household expenditure (in rupees)of manual workers in a city:

Expenditure (in Rs.)	Frequency	Expenditure (in Rs.)	Frequency
1000-1500	24	3000-3500	30
1500-2000	40	3500-4000	22
2000-2500	33	4000-4500	16
2500-3000	28	4500-5000	7

Find the average expenditure which is being done by the maximum number of manual workers.

Answer 1

We observe that the class $1500-2000$ has the maximum frequency $40$. So, it is the modal class such that
$l=1500,h=500,f=40,f_1=24,$ and $f_2=33$
$\therefore Mode=l+\frac{f-f_1}{2f-f_1-f_2}\times h$
$\Rightarrow Mode=1500+\frac{40-24}{80-24-33}\times 500$
$\Rightarrow Mode=1500+\frac{16}{23}\times 500=1847.826$