 Hello and welcome to the session. In this session we will discuss a question which says that the following data gives the number in thousands of trees planted in a particular area, calculate the plant by method of moving our bridges for a daily cycle. Also plot the graph. And this is the data which is given to us. And now we will start with the solution. Next we will draw a table for the given data. So we have drawn a table for the given data. And this the first column is representing the years. Second column is representing the number of trees planted in thousands. Then in the next column we will find the 10 yearly moving totals. In the next column we will find the 10 yearly moving average. And in the last column we will find the 10 yearly moving average centered. We will find the 10 yearly moving total. And the value is your first 10 years that is from the year 1990 to 1999 in between the fifth. Now here the fifth year is 95. So when you write the total of all these values here that is in between these seven. And now we will leave the first year value that is we will leave this back in 1991 2000. That is start the sixth and the seventh year that is in between we will write the total of all these values. And the total of all these values will give which is placed in between the sixth and seventh year which is the year 1995 and 1996. From the year 1992 the year 2000 that is start the values 92. And we will place the total in between the year 1996 and 1997 and the total of all these values is 902. Until this last year value is taken into account starting from the year 1993 2002. That is still in between the years 1997 and 1998 and the total is 910. The next 10 years that is starting from 91 we will add all the values and we will place the total in between the years 1998 and 1999. And the total is 910 that is starting from 93. We will add all the total in between the year 1999 and 2000. And the total is 900. Until in between the year 2000 and 2001 and the total is 888. We will place the total in between the year 2001 2002 and the total of all these values is now starting from 83 we will add all these values. The total in between the year 2002 2003 and the total is gives that this starting from 88 we will add all these values up to 94 and we will place the total in between the year 2003 2004 the year 2004 2005 and the total is 903 which is the last year value and we will place the total in between the year 2005 2006 moving average. We will divide the time we are moving total is 87 so the time we are moving average will be by time which is equal to 88.7 here it will be 89.2 where it will be 90 that is we will divide total 10 year moving average 910 divided by 10 will be 91.0 this will be 90.7 900 by 10 is 90.0 88.8 by 10 is 90.1 903 by 10 is 90.3 90.6 and then divided by 2 we will place it against the values we will add 2 by 2 the averages divide the total by 2 and place this value is equal to 89.7 by 2 and place this value against the averages divide the total of this value against the year 1998 and it will be 90.85 against the year 1999 and this value is 90.35 now for the next year the year 2000 then again we will take the next moving averages add them and divide the total by 2 9.05 and divide the total by 2 and place this value against the year 2003 89 points the total by 2 we are getting 90 value against the year 2004 the total by 2 we are getting 90.45 is 2005 first of all we will plot the actual values on the graph we will plot the years with the constant number of freeze planted in thousands on the graph now the first point that we will plot on the graph will be the year 1990 point on the graph which shows that in the year 1990 the number of freeze that were planted were 80,000 now the next point that we will plot will be the year 1991 with 82 point on the graph which shows that in the year 1991 the number of freeze that were planted were 82,000 we will plot all these points that is the year with the constant number of freeze on the graph so we have plotted these points we are getting a graph for the actual values so we will plot the years centered on the graph will be the year 1995 prior point on the graph 1996 with 89.7 prior point on the graph we will plot all these points the years with the constant on the graph on the graph now by joining all these points we are getting the graph for the trend values and this is also called the trend line so this is the solution of the given question and that's all for this session hope you all have enjoyed the session