 Hello and welcome to the session. In this session we will discuss the chain-based method to find index numbers. Now when year-to-year comparison is required, index numbers thus determined by a method known as chain-based method. Now in this method each year is taken as the base for the immediately next year and the first year itself being its own base. Now let us discuss it with the help of an example if the index numbers for the year 1975, 1976, 1978, 1979 and 1980 are to be constructed then we take 1975 as the base year for 1976 then 1976 as the base year for 1977 and so on. So we can say in this method each year is taken as the base for the immediately next year that is the next year to the year 1975 is 1976. So 1975 will be the base year for the year 1976 and similarly we can discuss it for the other years also and also the first year itself being its own base. Now here the first year is 1975 this means 1975 itself will be the base 1995. Now this type of index is called the chain-based index and such indices are suitable for the use in business where changes with reference to immediate past are important. Now let us discuss some of its advantages. Now the first advantage of chain-based index numbers is the new items are readily included and old ones dropped in their calculations and the second advantage is that such indices are more free from seasonal variations than the fixed base indices. Now let us discuss the steps of construction of chain-based index. In the first step the link relatives are computed by using the formula link-relatives is equal to the current year's price over the previous year's price into 100 and then in the second step the link-relatives are converted into chain-based index by using the formula which is chain-based index is equal to link-relatives of the current year into chain-index of the previous year over 100. Now let us discuss one example for this. Now in this we have to construct chain-based index from the following data. And in this the years are given to us and the corresponding price of a particular commodity in dollars is also given to us that is the years are given as 1955, 1956, 1957, 1958, 1959 and the corresponding price of a commodity in dollars is given as 50, 60, 65, 72, 76. Now for the construction of chain-based index first of all let us draw a table for the given data. So we have drawn a table for the given data here in the first column the years are given to us and in the second column we have written the corresponding prices of a particular commodity in dollars for the particular years and in the next column we will find the link-relatives and in the last column we will find the chain-based index numbers. And for finding out the link-relatives and the chain-based index we will use these formulas which we have discussed earlier. So the link-related for the year 1955 will be equal to the current year price which is 50 and let us take the previous year price as 50 as the first year will be the base year for itself. So the current year price is also 50 and the previous year price is also 50 into 100 which is equal to 100. Now here for the first year that is 1955 the chain-based index is equal to 100. Now for the year 1956 the base year will be 1955. So the link-related will be equal to the current year price which is 60 over the previous year price which is 50 into 100 and this is equal to 120. So the chain-based index will be equal to the link-related of the current year. Now the link-related of the current year that is the year 1956 is 120 into the chain-based index of the previous year which is 100 over 100 so this is equal to 120. Similarly for the next year the link-related will be equal to 65 over 60 into 100 which is equal to 108.33 and the chain-based index will be equal to 108.33 into 120 over 100 which is equal to 129.996. And for the next year that is the year 1958 the link-related will be 72 over 65 into 100 which is equal to 110.77 and the chain-based index will be equal to 110.77 into 129.996 which is equal to 143.997 and then for the year 1959 the link-related will be 22 into 100 which is equal to 105.997 which is equal to 52.003. To calculate the chain-based index by using the chain-based method session you have learnt about the chain-based method. At this completes our session, hope you have enjoyed the session.