 Hello and welcome to the session. In this session we will discuss a question which says that take a five-year period of moving average and determine short term oscillations for the final data also plot the graph for action and trend values. And this is the data which is given to us. And now we will start with the solution. Now when we take a five-year period of moving average and for this first of all we will draw a table for this given data. Now here we have drawn the table for the given data. Where the column is representing the years, the column tree is representing the number of students in thousands. And in the column tree we will find five yearly moving totals and in column tree we will find five yearly moving average. And in the last column we will find the short term oscillations. Now first of all we will find the five yearly moving totals. For this we will add the values of first five years that is starting from the year 1995 to the year 1999. So we will add these five values and we will write this total against the middle year which is the third year that is the year 1997. So we will write here 9 plus 12 plus 20 plus 23 plus 33 which is equal to 97. Next five years. That is we will add these values against the year 1998. So we will write here 12 plus 20 plus 23 plus 33 plus 90 which is equal to 107. So this last year's value is taken into account. So in the next which we get 121. Put the total against the year 2000 and we are getting 130. Now in the next step we will add total against the year 2002, 125. That is here it will be 97.5 19.4 which is equal to 21.4 142 by 5 is the short term better the values in column 2. 2012 20 19.4 minus 19.4 which is equal to plus 0.6 minus 21.4 grand point 6 minus 26 is minus 7 minus 28.4 is minus 2.4 minus 25 but on the graph will be the year 1995 with 9. Five point is that in year 1995 there were 9000 students. Now the next point that we will plot on the graph will be the year 1996 it on the graph. We are getting the graph for the actual values of the trend values on the graph. And we will plot on the graph will be the year 1997 we will plot the years. Plot will be the year 1998 with point on 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 this session.