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:
Expenditure (in C)
Number of families
$1000 - 1500$
$24$
$1500 - 2000$
$40$
$2000 - 2500$
$33$
$2500 - 3000$
$28$
$3000 - 3500$
$30$
$3500 - 4000$
$22$
$4000 - 4500$
$16$
$4500 - 5000$
$7$

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:

Filo · Accepted Answer

Mode: The class which has highest frequency.

In this case, class interval

1500 - 2000

is the modal class.

Now,

Lower limit of modal class,

l = 1500, h = 500, f_{1}, = 40, f_{0} = 24, f_{2} = 33

We know that,

Mode =

l + (\frac{f _{1} - f _{0}}{2 f _{1} - f _{0} - f _{2}}) \times h

= 1500 + (\frac{40 - 24}{2 ( 40 ) - 24 - 33}) \times 500

= 1500 + (\frac{16}{80 - 57}) 500

= 1500 + (\frac{16}{23}) \times 500

= 1500 + 347.826

Mode

= 1847.83

Lets take assumed mean,

A

as

3250

.

Class interval

= 500

N = 200, \sum f_{i} u_{i} = - 235

\overset{x}{ˉ} = A + h \frac{\sum f _{i} u _{i}}{N}

= 3250 + \frac{- 235}{200} \times 500

= 3250 + \frac{- 1175}{2} = 2662.5

Hence, the average expenditure is Rs

2662.50

.

Question Text	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 Type	Text solution:1
Upvotes	150

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