The quantity index number using Fisher's formula is a method of measuring the changes in the quantity of goods and services produced over time. It is a weighted average of the Laspeyres and Paasche price index numbers and is used to calculate the changes in the quantity of goods and services consumed.


The formula for Fisher's quantity index number is:

Quantity Index Number = √(Paasche Index * Laspeyres Index)

Where,
Paasche Index = (Current Year Prices * Current Year Quantities) / (Base Year Prices * Current Year Quantities)
Laspeyres Index = (Current Year Prices * Base Year Quantities) / (Base Year Prices * Base Year Quantities)


The quantity index number using Fisher's formula satisfies the unit test. This means that the index number is dimensionless and does not depend on the units of measurement used. The unit test is satisfied because the index is based on the ratios of quantities, not on the absolute quantities themselves.


The quantity index number using Fisher's formula satisfies the factor reversal test. This means that if the prices and quantities are switched, the resulting index number will be the reciprocal of the original index number. This property is useful in checking the consistency of the index over time.


The quantity index number using Fisher's formula does not satisfy the circular test. This test checks whether the index can be computed using different sets of base year and current year quantities and prices. Fisher's formula does not satisfy this test because it uses weighted averages of the Laspeyres and Paasche indices, which are not interchangeable.


The quantity index number using Fisher's formula satisfies the time reversal test. This means that if the time period is reversed, the resulting index number will be the reciprocal of the original index number. This property is useful in checking the consistency of the index over time.


The quantity index number using Fisher's formula is a useful tool for measuring changes in the quantity of goods and services produced over time. It satisfies the unit test and the factor reversal test, but does not satisfy the circular test. It also satisfies the time reversal test, which is useful in checking the consistency of the index over time.