Question

The frequency distribution table of agriculture holdings in a village is given below Area of land 1-3 3-5 5-7 No of families 20 45 80 Find the model agriculture holdings of the village​

Answer 1

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Answer 2

The modal agricultural holdings will be 5.608 units.

Step-by-step explanation:

Given:

Area of land= 1-3 3-5 5-7

No. of families= 20 45 80

To find:

The modal agricultural holdings (mode)

Formula:

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

Solution:

First, let's look at the modal class (class with the highest frequency)

The highest frequency is 80

∴ 5-7 is the modal class

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

where l=lower limit of the modal class=5

$f_{0}$=frequency corresponding to the modal class=80

$f_{1}$=frequency preceding the modal class=45

$f_{2}$=frequency succeeding to the modal class=0

Note-There's no frequency data after the modal class so we take it as 0

h=difference between the modal class's limit=2

Putting the values in the formula

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

          =$5+(\frac{85-45}{2(80)-45-0} ) 2$

∴Mode$=5+(\frac{35}{115} )2\\\\=5+\frac{70}{115} \\\\\frac{575+70}{115} \\\\\frac{645}{115\\}\\\\=5.608$

∴ The modal agricultural holdings will be 5.608 units.