 Hello and welcome to the session. In this session we will discuss a question that says that the table shows the number of paintings selected for the exhibition. That is, this is the table given to us. Drive a graph of these figures, calculate a set of moving averages, using the most number of observations, give reasons for your choice. Now in this question, since there are three terms, so we will calculate three term moving average. Now before starting the solution of this question, we should know a result. And that is, the pros and cons of calculating three yearly moving averages. Now five years, the data that is given to us, that is, the years and the particular values in those years are given to us and we will calculate three yearly total and three yearly moving average in these columns. For the three yearly total, in the first term, we will add the values of the first three years, that is the first, second and third year, and place the total against the middle year, which is the second year. So we will add the values of the first three years, that is, we will add A, B and C, and place the total against the second year. So this will be A plus B plus C. And the other thing is that in the next term, leave the first year's value, that is, we will leave A for the next three years. That is, for the second, third and fourth year. So now we will add B, C and D against the middle year, which is the third year. So we will write B plus C plus D against the third year and we will continue this process until the last year's value is taken for calculating the moving average. Now in the next step, on dividing the three yearly totals by three, you will obtain, that is, we will divide by three yearly totals. In this case, the three yearly total is A1, which is equal to 8, is it by 3? Here it will be A2 by 3, here it will be A3 by 3, and then we will plot the point as A1 by 3, third year as A4 by 3. We will work on the key idea and now we will start with the solution that is going to us. As we have discussed earlier, so we will calculate a table for the given data. So we have drawn a table and we are having ears in the second column months, in the third column number of paintings, in the next column we will calculate three-time moving total and in the last three-time moving average. Now using the result which is given in the key idea, that I have these values, the total against the middle term. We will put the total of these three values, 160 plus 324 plus 261, which we will divide this total by 3. So it will be by 3, which is equal to 3,3. These are the next three terms, which are these three terms, these three values. So we will put this total that is 192, which is equal to 777, the month of September. Similarly, for the final 77 divided by 3 will be equal to 259, this value. And then we will add three terms, which are these three terms against the middle term, which is the month of January. So we will put it here and 11. And on dividing this total by 3, that is 711 by 3, we will get 237. So this process until the last moving average. Now we will take and on dividing it by 3, we will get 246. Now next we will take that are these three values. And for some of these three values we will get 750. And on dividing it by 3, we will get 251.33. And 780 by 3 is 26 divided by 3 is equal to adding it by 3, it will be 261.33. Now next we will take 261 and on dividing it by 3 it will be, and on dividing by 3 it will be, it is equal to 274.33. And 795 by 3 is, we will take these three values, adding them it will be equal to 802. And 802 by it will be 790, until the last value, 1891. In the month of January the number of paintings are 160. We can represent it like this, that is for the month of January in the year 1991, the number of paintings are 160. Now in the year 1991, in the month of April the number of paintings are 324. We are representing it like this, in this, in the month of April the number of paintings are 324. We will plot all the actual values on the graph, the graph of the actual value, 1891 for the month of April, the moving of the graph we are having, 1991 for the month of September, it averages 259. For the month of September the moving average is 259. Now next for the month of January in the year 1992 the moving average is 237. So in the year 1992, in the month of January the moving average is 237. We have plotted all the trend values on the graph, enjoying all these points by obtaining the trend line. That is, this is the graph for the trend values. This is the solution of the given question and that's all for this session. Hope you all have enjoyed this session.