 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that the following table shows the age distribution of persons those have won gold medals in friendly games. Find the median age. The formula for calculating median in continuous series is given by md is equal to l plus i upon f multiplied by n by 2 minus c where n is the sum of the frequencies given by submission f, n by 2 is the median number is the lower limit of the median class is the cumulative frequency of the class just lower than the median class is the class interval of the median class f is the frequency of the median class with this key idea we shall proceed with the solution. The frequencies we are given are cumulative frequencies so first we shall convert them into absolute frequencies now we have divided the age groups between 0 to 10, 10 to 20, 20 to 30, 30 to 40 and 40 to 50 years there are three persons in the below 10 age group so number of persons in the age group from 0 to 10 will be 3 since there are 15 persons in the below 20 age group so in the age group 10 to 20 there will be 15 minus 3 that is 12 persons similarly we get 20 persons in the age group 20 to 30 11 persons in the age group 30 to 40 and 6 persons in the age group 40 to 50 now we shall calculate cumulative frequency in which the first entry will be same as that of frequency next will be 3 plus 12 that is 15 then 15 plus 20 that is 35 35 plus 11 that is 46 and 46 plus 6 that is 52 here some of all the frequencies that is submission of f is equal to 52 and we know that n is equal to submission f which is 52 and we know median number is equal to n by 2 so here median number is equal to 52 upon 2 which is equal to 26 now the cumulative frequency just greater than the median number that is just greater than 26 is 35 and therefore the corresponding class is 20 to 30 which is the median class now using the formula from the key idea where median md is equal to l plus i upon f into n by 2 minus c that is using the formula md is equal to l plus i upon f into n by 2 minus c where l is the lower limit of the class interval and here the interval is from 20 to 30 so it is equal to 20 i is the class interval of the median class from 20 to 30 so value of i will be 30 minus 20 which is equal to 10 f is the frequency of the class interval 20 to 30 which is 20 so f is equal to 20 c is the cumulative frequency of the class just lower than the median class which is 15 that is the value of c is equal to 15 now substituting all these values in the above formula we get median md is equal to l that is 20 plus i upon f that is 10 by 20 into n by 2 minus c that is 26 minus 15 which is equal to 20 plus 1 by 2 into 11 which gives 20 plus 11 by 2 which is equal to 20 plus 5.5 that is median is equal to 25.5 hence the median age is 25.5 years which is the required answer this completes our session hope you enjoyed this session.