 Hello and welcome to the session. In this session we will discuss a question which says that the following table gives number in legs of the central cars passing from Tone Bridge from late 2005 to June 2007. Now this data is given to us. Now we have to construct the table showing the 12 monthly moving averages and draw a graph to show the print. Now we will start with the solution. Now we will construct the table showing the 12 monthly moving averages for this given data. So we will draw the table for the given data. Now we have the first column is representing the years and the second column is representing the months in the particular years and in the next column we have the number of cars in legs. Then in the next column we will find the 12 monthly moving total. In the next column we will find the 12 monthly moving average and in the next column we will find the 12 monthly moving average centred. First of all we will find the 12 monthly moving total. We will add the values for the first 12 months that is starting from the data which is given to us that is given from the month of May in the year 2005. So starting from the month of May in the year 2005 the month of April in the year 2006 that is start of the first month and the year 2006 as the 12th month we will check the 6th and the 7th month. Now the 6th and the 7th month is the month of October of November in the year 2005 7th month November in the year 2005. The values we are getting the total is 325 that we will leave the value for the first month and now use for the next 12 months. That is starting from the month of June in the year 2005 the month of May in the year 2006 that are the values starting from 23 21 and we will place the value in between the month of November and the month of December in the year 2005 and the total of the 325. Now we will leave this value the values for the next 12 months that is starting from the month of June the month of June in the year 2006 it is free and we will place the total in between the month of December in the year 2005 and the month of January in the year 2006. Now for these values is 325 and now we will leave this value and add the values for the next 12 months that is starting from the month of August in the year 2005 add all these values in between the month of January and February in the year 2006 and the total is 321. Add the values for the next 12 months month of February and March in the year 2006 and the total of all these values is now we will add the values for the next total in between the month of March and April in the year 2006 and the total is 324 year 2006 and the total is until this last month's value which is given to us in the data that is for the month of June in the year 2007 is taken into account. Now we will add the values for the next 12 months that is starting from 26 so in between the months of May and June in the year 2006 and the total is we add the values for the next 12 months that is starting from 28 we will add all the values in the month of June or July in the year 2006 and the total is 332. Now starting from 28 we will add the total in between the month of July and August in the year 2006 and the total is 330 between the month of August and September in the year 2006 and the total is 327 and the total is 331 that is for the next 12 months that is starting from 23 we will add and we will place the total in between the months of November and December in the year 2006 and the total is 338 we will place the total in between the month of December in the year 2006 and the month of January in the year 2007 and the total is under this last month's value is taken into account the 12 monthly moving averages for calculating this we will divide the 12 monthly moving total now here the 12 monthly moving total is 325 so the 12 monthly moving by 12 which is equal to 27.08 also 27.08 here also it will be 27.08 now 321 by 12 26.75 7 by 12 is 27.227 332 by 12 is 7 by 12.25 331 by 9.42 monthly moving average center center we will add month that is here November that will be 27.08 0.08 whole upon 2 27.08 the next step consider the next moving averages and divide the total by 2 and place it against the month of December in the year 2005 and this value will be 27.08 now consider the next moving averages case the month of January in the year 2006 and it will be 26.91 similarly we will take the next moving averages and dividing the total by 2 against the month of February in the year 2006 705 now consider push in the year 2000 moving averages and for these moving averages this value will be 27.12 and we will place it against in the year 2006 now for the next one and dividing the total by 2 we will place this value against the month of May in the year 2006 and this value is 27.12 now consider the next moving averages and divide the total by 2 and place it against the month of June in the year 2006 and the value is 27.33 and now consider the next moving averages and divide the total by 2 the month of July in the year 2006 and this value is 27.00 now for the next moving averages 27.05 and we are placing it against the month of August in the year 2006 now for the next moving averages we are getting this value as 27.45 this value against the month of September in the year 2006 now consider the next moving averages add them and divide the total by 2 the month of October in the year 2006 and this value is 27.00 now for the next moving averages 955 and we are placing it against the month of November in the year 2006 now consider the next moving averages against the month of December in the year 2006 on this value is 28.79 and now we will draw a graph for the actual friend values on the graph we will plot the months in the particular years with the number of cars on the graph will be the month of May in the year 2021 five point on the graph in the month of May told which were 21 years now the next point we will plot on the graph will be the month of June in the year 2005 with 23 so this is the required point on the graph which means in the month of June in the year 2005 the number of cars the months in the particular years for plotting the actual values on the graph so we will plot all these points on the graph we have plotted all these points on the graph now by drawing all these points we are getting the graph for the actual values and now we will plot the friend values on the graph let us draw these values of 12 monthly moving average centered now for plotting the trend values we will draw the months in the particular years with the 12 monthly moving average centered that is the first point that we will plot on the graph will be the month of November in the year 2.1 so this is the required point on the graph now the next point will be the month of December in the year 2021 this is the required point on the graph plot the rest of the months in the particular years with the prime monthly moving average center so we have plotted all these points on the graph now by drawing all these points we are getting the graph for the trend values and this is also called the trend line again a question and that's all for this session hope you are having enjoyed the session