Weighted average-of-relatives index

In case of average of weighted relatives, price relative of each commodity is multiplied by the weight of that commodity and the sum of these products is divided by the sum of weights of all the commodities. Weighted average-of-relatives index can be calculated by taking arithmetic mean as well as geometric mean as average. If arithmetic mean is taken as average then formula will be:

 

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Geometric mean is sometimes used as an average. The weighted average-of-relatives (G.M.) is computed by the formula

 

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Problem: For the data given below in the table, construct weighted average of relative’s index using; (a) Arithmetic mean as the average (b) Geometric mean as the average while taking 1993 as base.

 

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Solution:

 

Arithmetic mean as the average

The Weighted average-of-relatives index is calculated by taking mean as average. This calculation is shown in the table given below.

 

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Geometric mean as the average

 

Since Weighted average-of-relatives index is calculated by taking geometric mean as average therefore the formula of geometric mean will be used. The calculation is shown in the table given below.

 

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Summary of Results

 

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6 responses to Weighted average-of-relatives index

I need to understand when weighted averages can be applied and when unweighted averages can be applied.

To my earlier question i understand now that when the weight is given we may apply the weighted average and when not we apply un weighted. Can you still clarify in its application. An example that we make it clear unwhat scenerio to use weighted and unweighted.

Thank you though. This is a great job.

1) When the Weighted Average of relative is greater than Weighted Aggregate of relative, what is the implication?

2) When the Weighted Average of relative is less than Weighted Aggregate of relative, what is the implication?

3) When the Weighted Average of relative is equal to Weighted Aggregate of relative, what is the implication?

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