 Hello and welcome to the session. In this session we will discuss the comparison of index numbers by the use of geometric mean and arithmetic mean. Now as we know that in the construction of index numbers we are concerned with the ratios or relative changes. Now the geometric mean is considered to be the best for the construction of index numbers as this is most suitable for measuring the relative changes. The beautiful drawback of difficulties of computation in place of geometric mean, unsymmetric mean is most often used in the construction of index number. Even index number based on arithmetic mean suffers from all different quantities that an arithmetic mean has. Hence, geometric mean should be preferred over other measures of subterranean currency. Let us discuss one example. Now here this data is given to us and here we are taking the year 1985 as the base year. Now we do that at the base year we take the price rate of 100. Now for the commodity rate for calculating the price related for the year 1986 we are here using the formula that is price related is equal to the current price over base price into 100. So for the year 1986, early 1985 as the base year so price related will be equal to the current price which is 12 over the base price which is 24 into 100. Which in calculating will be equal to for the commodity A the price related for the year 1986 is we have calculated that the other cases are also and in this table the commodities are given to us as A, B and the price in dollars is given as 24 and 50 and also the price related for the commodity A is 100 and for B it is also 100 and for the year 1986 the price in dollars for the commodity A is 12 for B it is 75 and the corresponding price relatives are 50 and 150 and the year 1987 the price in dollars is 12 and 100 and the corresponding price relatives are 15 and 200 and then in the next we have calculated the total of the price relatives in the particular years and then we have got which is equal to the sum of the observations that is 200 over the number of observations which are 2 so 200 over 2 is 100 and then for the year 1986 the mean of the price relatives is 200 by 2 which is 100 and for the year 1987 the arithmetic mean of the price relatives is 222 by 2 which is 125 and then we have got the geometric mean for the year 1985 the geometric mean of price relatives is square root of root into 100 which is 100 and then for the year 1986 the geometric mean of price relatives is square root of 15 into 150 which is equal to 86.6 then for the year 1987 the geometric mean of the price relatives is square root of 15 into 200 which is equal to 100 now here you can see that the base year is 1985 now for the year 1986 by 15 percent the year 1985 the price of the commodity A was $24 much in the year 1986 the price of the commodity A $12 that means the price of the commodity A has gone down by 50% to B has gone up by 50% that is in the year 1985 the price of the commodity B was $50 1986 the price of the commodity B it means that the price of the commodity B has got up by 50% you can also see that the arithmetic mean has shown no change in the index number but the geometric mean a change that the average price has gone down by 50% price rather it can be compensated by 100% price by the geometric mean observed by the arithmetic mean as the arithmetic mean is showing no change so we can write that the geometric mean of better measure of the year 1987 here it is clearly visible that the price of the commodity A by 15% well you can see that in the year 1985 the price of the commodity A was $24 and in 1987 it means the price of the commodity A has gone down by 50% the price of the commodity B doubled in comparison to the year 1985 so we can say that the price of the commodity B or it has gone up by 100% now here the two qualities are of equal importance and there should not be any change in the value of index number of 1987 from that of 1985 if the price of one commodity was down by 50% and the other rises by 100% then there exists no change in the price level but in this case you can see that the other shows an increase of 0% whereas the geometric mean does not favor any change in the price in 87 in comparison to that of 1985 the geometric mean is 100 for both the years and increase of 25% then the price of A has gone down by 50% and the price of B has gone up by 100% there should not be any change in the value of index number of the year 1987 from that of the year 1995 but in this the arithmetic mean is showing 25% increase and geometric mean is showing no change in the price of 1987 in comparison to that of 1985 hence we can say that the geometric mean gives a correct measure so we can say that in the construction of index numbers geometric mean should be preferred of central currency the correct measure so in this fashion you have learned about the comparison of index numbers by the use of geometric mean and a symmetric mean this completes our session hope you all have enjoyed this session