 Hello and welcome to the session. In this session we discuss the following question which says find the median for the following data. This is the data given to us in which we are given the variant and the frequency. First let's recall how we find the median for the given data. Then we are given the total frequency to be n. Then if n is odd then we have the median is equal to the size of n plus 1 upon 2th item and if n is even then the median is given by half of the size of n upon 2th item plus the size of n upon 2 plus 1th item. This is the key idea to be used in this question. Now let's proceed with the solution. This is the data given to us. When we need to find out the median our first step would be that we arrange the data or we arrange the terms in an ascending or descending order. Now as you can see the given data is already arranged in ascending order. Next we will prepare a cumulative frequency table. We will write the data again that is the variant and the frequency again in this cumulative frequency table. For the variant 3 the frequency is 3, 5, it's 6, for 10 it's 5, for 12 it's 4, for 15 it's 10 and for 20 it's 3. So let's calculate the cumulative frequencies. This would be 3. Now for the next variant the cumulative frequency would be 3 plus 6 that is 9 and for the variant 10 the cumulative frequency would be given by 5 plus 9 and that is 14. For the variant 12 the cumulative frequency would be 4 plus 14 that is 18. For the variant 15 cumulative frequency is 10 plus 18, 28. For the variant 20 the cumulative frequency is 3 plus 28 that is 31. So now we have the total frequency that is n is equal to 31. Now this m equal to 31 is odd. So using the key idea we have that the median is given by the size of n plus 1 upon 2th item that is median is equal to the size of 31 plus 1 upon 2th item that is equal to size of the 16th item. Now in the table as you can see that we don't have any cumulative frequency as 16. So we will look for the cumulative frequency more than 16 and that would be 18. Now for 18 the corresponding variant is 12. So we would say that the size of the 16th item is 12. Thus we get the median is equal to 12. So this is our final answer. This completes the session. Hope you have understood the solution for this question.