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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 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 |
Given:
The given data gives the distribution of total monthly household expenditure of 200 families of a village.
To do:
We have to find the modal monthly expenditure of the families and the mean monthly expenditure.
Solution:
The frequency of the given data is as given below.
We know that,
Let the assumed mean be $A=2750$.
Mean $=A+h \times \frac{\sum{f_iu_i}}{\sum{f_i}}$
Therefore,
Mean $=2750+500\times(\frac{-35}{200})$
$=2750-2.5\times35$
$=2750-87.5$
$=2662.5$
The mean of the given data is Rs. 2662.50.
We observe that the class interval of 1500-2000 has the maximum frequency(40).
Therefore, it is the modal class.
Here,
$l=1500, h=500, f=40, f_1=24, f_2=33$
We know that,
Mode $=l+\frac{f-f_1}{2 f-f_1-f_2} \times h$
$=1500+\frac{40-24}{2 \times 40-24-33} \times 500$
$=1500+\frac{16}{80-57} \times 500$
$=1500+\frac{8000}{23}$
$=1500+347.83$
$=1847.83$
The mode of the given data is Rs. 1847.83.
The mean and mode of the above data are Rs. 2662.50, 65 and Rs. 1847.83 respectively.
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