M = ( )( )( ) = . When the number of items is three or more the task of multiplying the numbers and of extracting the root becomes excessively difficult. To simplify calculations, logarithms are used. Geometric mean is calculated as follows: log log log ........
log GM (or ) log log GM = Σ GM Anti log log Σ where n is number of observation. (i) In discrete observation GM Anti N log log Σ ; where N = Σ (ii) In Continuous observation GM = log log Anti N m / ; E ; where m is midpoint and N = Σ Example . Daily income (in Rs) of ten families of a particular place is given below. Find out GM , , , , , , , , , .
G M Anti log log Σ ; where n = G M Anti log = Anti log( . GM = . - - Example . Calculate the geometric mean of the data given below giving the number of families and the income per head of different classes of people in a village of Kancheepuram District.
Class of people No. of Families Income per head in (Rs) Landlords Cultivators Landless labourers Money- lenders School teachers Shop-keepers Carpenters Weavers Calculation of Geometric Mean Class of people Income per head in ( ` ) No of Families log X f log X Landlords . . Cultivators .
. Landless labourers . . Money- lenders .
. School teachers . . Shopkeepers .
. Carpenters . . Weavers .