 Hello and welcome to the session. In this session we will discuss the question which says that for the given data compute index numbers for various years by taking 1918 to 1983 as base period and the data is given to us in which the years are given as 1980, 1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989 and 1990 and the corresponding prices of the commodity are given as 8, 9, 11, 12, 13, 15, 17, 19, 20, 21, 23 and 25. Now before starting the solution of this question we should know a result and that is for a single commodity the index number for each year is the same price related that is P1 over P0 in 200 where P1 denotes the current year prices P0 denotes the base year prices of the given commodity in different years. Now this result will work out as a key idea for solving out this question and now we will start with the solution. Now here for the given data we have to compute the index numbers for various years by taking 1918 to 1983 as the base period Now here the base period is not a single year but here it is given to be a period 1980 to the year 1983. Therefore we take the average of the prices in the year 1980, 1981, 1982 and 1983 as the base period the average is equal to Now for the year 1980 the price is 8, for 1981 it is 9, for 1982 it is 11 and for 1983 it is 12. So the average will be equal to the sum of observations over the number of observations which is 8 plus 9 plus 11 plus 12 over time which is equal to 40 upon 4 which is equal to 10. And now let us calculate the index numbers 1880 to 1983. Now here you can see that the price of a single commodity is given for different years and from the key idea we know that for a single commodity the index number for each year is same as the price related. So now let us draw a table for the given data to compute index numbers into 1983 as the base period. So we have drawn a table for the given data column we have written the years in the second column the prices of a commodity in different years and in the last column we will find the index numbers which are same as the price related P1 over P0 into 100. Now we have calculated the base price is equal to 10 that is P0 is equal to 10. Now the prices of the commodity in different years is denoted by P1. So for the year 1980 the index number will be equal to P1 which is 8 over P0 which is 10 into 100 which is equal to 8. Then for 1981 it will be 9 over 10 into 100 which is equal to 90. Then for the next year the index number will be equal to 11 over 10 into 100 which is equal to 110. Then for 1983 it will be 12 over 10 into 100 which is equal to 120. For 1984 index number is 13 over 10 into 100 which is equal to 130. Then for 1985 index number is 15 over 10 into 100 which is equal to 150. Then for 1986 it is 17 over 10 into 100 which is equal to 170. Then for next year it is 19 over 10 into 100 which is equal to 190. Then for 1988 the index number is 21 over 10 into 100 which is equal to 210. Then for 1989 the index number is 23 over 10 into 100 which is equal to 230. And for the year 1990 the index number is 25 over 10 into 100 which is equal to 250. So in this way we have computed the index numbers for various years by taking 1918 to 1983 as the peace period. So this is the solution of the given question and that's all for this session. Hope you all have enjoyed the session.