Question

The frequency distribution table of agricultural holdings in a village is given below: Find the modal agricultural holdings of the village.

Answer 1

ANSWER

The class corresponding to this frequency is 5–7. So, the modal class is 5–7. Hence, the modal agricultural holdings of the village is 6.2 hectares.

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Answer 2

Correct Question:

The frequency distribution table of agriculture holdings in a village is given below:

Area of land (in hectares): 1-3 3-5 5-7 7-9 9-11 11-13

Number of families: 20 45 80 55 40 12

Find the modal agricultural holdings of the village.

Answer:

The modal agricultural holdings are 6.2 hectares.

Step-by-step explanation:

Given:

data in hectares and no. of families

To find:

the modal agricultural holdings

Solution:

We have to find the mode for the given data. Hence, we look at the highest frequency here. It is 80 in this case.

So the corresponding class 5-7 will be our modal class.

Now, Mode= $l+(\frac{f_{1}-f_{0} }{2f_{1}-f_{0} -f_{2} }) X h$

where $l$= lower limit of the modal class = 5

$f_{1}$= frequency of the modal class= 80

$f_{0}$= frequency of the class preceding the modal class= 45

$f_{2}$= frequency of the class succeeding the modal class= 55

$h$= difference between the upper and lower limit of modal class= 7-5 = 2

Substituting all the values in the formula

Mode= $l+(\frac{f_{1}-f_{0} }{2f_{1}-f_{0} -f_{2} }) X h$

∴ Mode = $5+(\frac{80-45 }{2(80)-45-55} }) X 2$

∴ Mode = $5+(\frac{35 }{160-100} }) X 2$

∴ Mode = $5+(\frac{35 }{60} }) X 2$

∴ Mode = $5+(\frac{35 }{30} })$

∴ Mode = $6.2$

∴ Mode = 6.2 hectares

Thus, the modal agricultural holdings in the village will be 6.2 hectares.

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