Question

Calculate the fishers ideal index from the following data

Answer 1

Given:

$A \ \ 6 \ \ 50 \ \ \ 10 \ \ 56 \\B \ \ 2 \ \ 100 \ \ \ 2\ \ \ 120 \\C \ \ 4 \ \ 60 \ \ \ \ 6 \ \ \ \ 60\\D \ \ 10 \ \ 30 \ \ 12 \ \ 24$

To find:

fishers ideal index=?

Solution:

In the question, the is missing data is given in the given part. Please find it.

In the first step, we assign the numbering to the given data.

    $A_0 \ B_0 \ A_1 \ B_1$

$A \ \ 6 \ \ 50 \ \ \ 10 \ \ 56 \\B \ \ 2 \ \ 100 \ \ \ 2\ \ \ 120 \\C \ \ 4 \ \ 60 \ \ \ \ 6 \ \ \ \ 60\\D \ \ 10 \ \ 30 \ \ 12 \ \ 24$

In the second step, we multiply the numbering and add its value, which is defined as follows:

   $A_0 B_0 \ \ A_1B_0 \ \ A_0B_1 \ \ A_1B_1$

$A \ \ 300 \ \ 500 \ \ \ 336 \ \ \ 560 \\ B \ \ 200 \ \ 200 \ \ \ 240\ \ \ 240 \\C \ \ 240 \ \ 360 \ \ \ 240 \ \ \ 360\\D \ \ 300 \ \ 360 \ \ \ 240 \ \ \ 288$

$\Sigma \ \ 1040 \ \ 1420 \ \ 1056 \ \ 1448$

Calculating L and P:  

L →Laspeyre's index

P → index Paasche's index

$L = \frac{\Sigma A_1B_0 }{ \Sigma A_0B_0 } \times 100$

   $= \frac{1420}{ 1040}\times 100\\\\ = \frac{142}{ 104}\times 100\\\\ = 1.365\times 100\\\\ = 136.5$

$P = \frac{\Sigma A_1B_1 }{ \Sigma A_0B_1 } \times 100$

$= \frac{1448}{ 1056}\times 100\\\\ = 1.371\times 100\\\\ = 137.1$    

Using the formula for  fisher's ideal index $= \sqrt{ L\times P }$

                                                                     $= \sqrt{ (136.5 \times 137.1)} \\\\ = \sqrt{18714.15}\\\\ = 136.79$