 Hello and welcome to the session. In this session, first of all we will discuss drawbacks of unrated index numbers. Now the first drawback of unrated index numbers is that drawback of unrated index numbers, the rate of each commodity is considered as 1. That is each commodity has equal importance that in actual practice it is spent on all items are not same. Now here for the creation the number of items, the quantities choose the value of index numbers. These are coded in different units and give no indication of the relative importance each item and also the units in which prices are given affect the value of index very much. Now let us discuss the units of goods. Now in simple index numbers all commodities are given equal importance but in actual practice all commodities do not have equal importance. For example, for a consumer weed is more important than vegetables or prices. Loads are more important than a video. Now to show the relative importance of different commodities, weeds on some definite basis are used. Therefore when the index numbers are constructed taking into consideration the importance of different commodities then they are called unrated index numbers. Now, weeds are a sign economic importance of the commodities. Now the weights can be production figures, consumption figures, sales figures etc. Now the method of construction of index number decides the type of weight to be used. Now in aggregate method we use quantity weights which means the amount of commodity produced, distributed or consumed in a certain period. And in case of price relatives value weights. Now a value weight combines price with quantity produced, sold, distributed and from which time period we should take the weights. The basic quantities or current quantities or average or base and current year or some such combinations of these methods are used to decide the time period to take the weights. Now let us discuss the types of weighted index numbers. Now the weighted index numbers are of two types. First is aggregate index numbers and aggregate method. Now in this method commodities are assigned weights on the basis of quantities purchased and there are some criteria on which the weights are assigned. So the criteria on which the weights are assigned are on the basis, the current year quantity then on the basis of base year quantity and then current base years or we can say the weights, the weight of each item are given with the base prices P1 then the index number based on weighted aggregates is given by is equal to summation into W over summation of P1 into W into 200. Now when the quantities of the base year taken as weights then the weighted index number is constructed by using the formula P01 is equal to summation of P1 into Q0 over summation of P0 into Q0 into 100. Now let us discuss one example for this and in this we have to calculate the weighted index number for the year 1918 using weighted aggregates method from the following data. Now in the first column the commodities A, B, C and D are given to us and in the second column the particular quantities are given as 3, 2, 4, 7 is in dollars for the particular commodities in the year 1970 is given as 5, 10, 8, 3 it is given as 7, 11 and 1980 is the grant year. So the prices for the year 1980 are the current prices which are denoted by P1 and for the year 1970 the prices are the base prices which are denoted by P0. Now to find the index number we have to find the value of summation P1 into W and summation of P1 into W. Now for calculating this in this table P1 into W and P0 into W so we have made two columns and in this column we have the different values of P0. So here P0 into W will give 15 for the commodity B W into P0 will be equal to 20 and for C it will be 4 into 8 which is particular and then for D it will be 7 into 3 which is 21. Now in the last column we will find P1 into W. Now these are the different values of P1 that is the current prices and we have the different values of the weights. So for the commodity A P1 into W will be 21 for B it will be 11 into 2 which is 22 for C it will be 12 into 4 which is 48 and then for B it will be 6 into 7 which is 42. Now on adding the different values of P0 into W we are getting summation of P0 into W is equal to 58 and here we are getting summation of P1 into W is equal to 133. Now the index number that is the weighted index number P01 will be equal to summation of P1 into W over summation of P0 into W into 100 which is equal to 133 over 88 calculated index number by applying the weighted aggregates method. Now we can discuss the weighted average of price-related method. Now in this method the price-related we have first of all the price-related for the current year are calculated on the basis of the basic prices of the commodities. When the base and current prices of a number of items along with weights of quantities are given then the weighted average is given by which is equal to summation of P1 over P0 into 100 the whole to W whole upon summation W which is equal to summation of price-related into the whole upon summation of W into X over summation of W summation of P1 over P0 into 100 the whole. P0 is the price of commodity in the base year and Q0 is the quantity of the commodity in the base year then its weight is given by P0 into Q0 so the above formula will become that is P1 over P0 into 100 the whole into now the weight is given by P0 into Q0 so in place of weight we will write P0 into Q0 whole upon summation of P0 into Q0. Weins are not given when we find the base year values P0, Q0 and consider them as weights. To discuss an example we have to calculate the weighted index number for the year 1991 from the given data by using weighted average of price-related method. The first column the items A, B and C are given to us then in the next column the price in dollars in the year 1990 which is taken as the base year for the year 1991. So the prices in the base years as denoted by P lot and the different values of P0 are given as 120, 180 and 20 and the prices in the current year are given as P1 and the different values of P1 are 150, 230 and the quantity in the base year that is the year 1990 are denoted by Q lot and the different values of Q0 are given as 10, 15 and 5. In this equation weights are not given so for this write Q0 for each commodity and consider them as weights. We will find out the weights which are denoted by W P0, Q0. The commodity A P0, Q0 will be equal to 1200 then for B it will be equal to Q0, Q0 will be equal to we will calculate the price related x which is equal to P1 over P0 into 100 and in the last W into x. So first of all let us calculate the different values of x P1 which is 150 over P0 which is 120 into 100 and on calculated this will be 125 for the commodity B it will be 200 over 180 into 100 which is 111.11 and for commodity C it will be equal to 30 over 20 into 100 which is 15 W into x. So for the commodity A W into x will give 150,000 now for the commodity B W into x will be equal to 299,997 and for the commodity C W into x will be equal to 15,000. On adding the different values of W into x we get summation of W into x is equal to 64,997 and on adding the different values of W we get summation of W is equal to 4000. Now the weighted index number P01 will be equal to summation of W into x over summation W. So here P01 is equal to summation of W into x over summation W which is equal to 7 over 16.25. So we have calculated the index number for the year 1991 with the year 1990 as the base year by using the weighted average of price related method. Now you have learnt about the drawbacks of unweighted index numbers and then weighted index numbers and methods of constructing weighted index numbers. So this completes our session hope you all have enjoyed the session.