 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that from the following data calculate median q1, q3, 8 deciles and 25th percentile. For simple distribution, median is equal to size of n plus 1 by 2 item, lower quartile q1 is given by size of n plus 1 by 4th item, upper quartile q3 is given by size of 3 by 4 into n plus 1th item, 8th decile, d8 is given by size of 8 by 10 into n plus 1th item and 25th percentile is equal to size of 25 by 100 into n plus 1th item where n is the number of items. With this key idea let us proceed with the solution. Since we are given simple distribution of data, so first we shall arrange this data in ascending order. So after arranging the given data in ascending order we get the given data as follows. Here the total number of elements that is n is equal to 11 and from the key idea we know that median is given by size of n plus 1 by 2th item. Therefore median is equal to size of n plus 1 by 2th that is 11 plus 1 by 2th item which is equal to size of 6th item and from the series 6th item is 40. Therefore median is equal to 40. Now lower quartile q1 is given by size of n plus 1 by 4th item that is lower quartile q1 is equal to size of n plus 1 by 4th that is 11 plus 1 by 4th item which is equal to size of 12 by 4th item which is equal to the size of 3rd item and size of 3rd item from the series is 25. Thus lower quartile q1 is equal to 25. Now upper quartile q3 is given by size of 3 by 4 into n plus 1th item that is upper quartile q3 is equal to size of 3 by 4 into n plus 1 that is 11 plus 1th item which is equal to size of 3 into 12 by 4th item which is equal to the size of 9th item and from the series the 9th item is 60. Therefore upper quartile q3 is equal to 60. Now 8th decile d8 is given by size of 8 by 10 into n plus 1th item. Therefore 8th decile d8 is given by size of 8 by 10 into n plus 1th that is 11 plus 1th item which is equal to size of 8 by 10 into 12th item which is equal to size of 96 by 10th item which gives the size of 9.6th item which is further equal to size of 9th item plus 0.6 into size of 10th item minus 9th item and from the series 9th item is 60 and 10th item is 66. So we have 8th decile d8 is equal to 9th item that is 60 plus 0.6 into 10th item that is 66 minus 9th item that is 60 which implies d8 is equal to 60 plus 0.6 into 6 which implies d8 is equal to 60 plus 3.6 Thus 8th decile d8 is equal to 63.6. Now 25th percentile is given by size of 25 upon 100 into n plus 1th item that is 25th percentile is equal to size of 25 upon 100 into n plus 1th item that is 11 plus 1th item 25th percentile p25 is equal to size of 25 upon 100 into 12th item or p25 is equal to size of 3rd item from the series the 3rd item is given as 25. Therefore p25 that is 25th percentile is given by 25. Thus median is equal to 6, upper quartile q3 is equal to 60, lower quartile q1 is equal to 25, 8th decile d8 is equal to 63.6 and 25th percentile p25 is given by 25 which is the required answer. This completes our session. Hope you enjoyed this session.