 Hello and welcome to the session. In this session we will discuss a question which says that the table below gives deterrence of consumption of coal in the generation of electricity in a thermal power station in each quarter for the years 1995 to 1997. To calculate four quarterly moving averages, show these moving averages on a graph. Now before starting the solution of this question we should know a result. And that is the procedure for calculating four yearly moving averages. For this we will draw a table and in this the values for the particular years will be given to us and we will find the four yearly moving total, the four yearly moving average and the four yearly moving average centre. Find four yearly moving total. For this we will add the values of these four years from in between the second and third years. So we will add these four and we will place the table in between second and third year plus B plus C plus D here in between second and third year and let it name as A1. Next four years, that is we will add these four values and we will place the total in between third and fourth years. So we will place the total of these values which will be B plus C plus D plus E here and let it name as A2. Next year is taken into account. Now we will calculate for yearly moving average. Now for calculating this we will divide four yearly moving totals that is A1, A2, A3 and A4 by 4 and we will get four yearly moving averages. So for this it will be A1 by 4 and let it be M1. Here it will be A2 by 4, let it be M2 and A3 by 4, let it be M3. Now we will calculate four yearly moving average centered. For this we will add against the third year. So we will write here M1 plus M2 whole upon 2 and let it be B1. It will be M2 plus M3 divided by 2 and place it against the fourth year. So it will be M2 plus M3 whole upon 2 and let it be B2. M4 whole upon 2 and let it be B3. Now for the graph B1 the fourth year with B2 with B3 bring to a line. We will work out as a key idea for solving now we will start with the solution. Now where this table is given to us and we have to calculate four quarterly moving averages. Now using this result which is given in the key idea we will make a table for the given data. We have made a table in which the first column shows the years, second, quarters, third, all years and turns and we have to find four quarterly moving total, four quarterly moving average and four quarterly moving average centered. In total we will add the values for the first in between plus 14 plus 12 equal to 47. Now next we will leave the first value and we will add the values for the next four quarters. That is we will add these four values in between third and fourth quarter. So here it will be 14 plus 12 plus 11 plus 13 which is equal to 50 in between fourth and 1995 and first quarter of the year 1996. So it will be 12 plus 11 plus 13 plus 19 which is 55. These four values and place the total in between second and first quarter will be equal to 61. Now next we will add and place the total in between second and third quarter. Adding one we will get 67 and on the next step we will add quarter. So it will get 70. Now in the next step of year 1996 and first quarter of year 1997 and the total of these four values will be 74. Then in between first and second quarter we will place the total in between second and third quarter. So it will be 80 in total by four. So in this case it will be 12 by 4 which is equal to 11.75 and for this it will be 50 by 4 which is equal to 12.5 and here it will be 55 by 4 which is equal to 13.75 and therefore it is 15.25 75 70 by 14.5. 74 by 4 is 18.5 and therefore it is 19.25. And now for the fourth part we will move in every center and we will divide them by two and place this value against the third quarter. So it will be 11.75. Calculating will give 0.125 which is equal to 12.1. Similarly for the next we will add and divide by two it will give 13.125 and we will place this value against the fourth quarter. So it will be 13.125. Now next we will add these two values and divide them by two and we will place this value against the first quarter of the year 1996. And calculating this will be 14.5. Now next divide them by two and place this value against the second quarter of the year 1996 and it will give 16. And next we will use and divide by two and place this value against the third quarter. So it will give 17.125. Now taking these two values we will get 18. Now next we will take these two values and we will get 18.875. And now next we will take these two values and we will get 19.625. Now we will round up all these values. So this will be 13.1. It will be 14.5. This is 16 and this will be 17.1. This is 18 and it will be 18.9 and this will be 19.6. The actual and the trend values on the graph. The graph that is the first part which is the coin used into the third quarter with 12 on the graph. That is the third quarter. We will plot all these points on the graph. We will get the graph that is the third quarter with so this is the required point on the graph. The quarter with 13.1. So this is the required point that is the fourth quarter of the year 1995 with 13.1. The quarter of the year 1996 with 14.5. The quarter of the year 1996 with 16. The third quarter with 17.1. The quarter of the year 1997 with second quarter of the year 1997 with 19.6. All these points on the graph. We will get the graph to show the given question and that's all for this session. Hope you all have enjoyed the session.