 Hello and welcome to the session. In this session we discuss the following question which says daily wages of 31 workers in a factory are given below. Find the median and the mean using empirical formula calculate its mode. In this table we are given the daily wages and the number of workers. Before we move on to the solution let's recall the formula for mean, median and mode. Consider x1, x2 and so on up to xn be in observations with f1, f2 and so on up to fn as their frequencies respectively. Then we have mean is equal to summation xi fi i goes from 1 to n upon summation fi i goes from 1 to n. Now if we have n is the total frequency then median is equal to the size of n plus 1 upon 2th item. If we have n is odd and median would be equal to half of the size of n upon 2th item plus the size of n upon 2 plus 1th item. If we have that n is even and the empirical formula for mode is given by 3 times median minus 2 times mean. This is the key idea to be used in this question. Now we move on to the solution. First we will make a table to find the median and the mean. So in this table we have the daily wages that is xi, number of workers, corresponding frequency fi, cumulative frequency and the product of xil fi. We have xi as 10, 20, 30, 40 and the corresponding frequencies fi as 5, 10, 6, 10. Now the cumulative frequencies are given by 5, then 10 plus 5, 15, then 15 plus 6, 21, 21 plus 10, 31. And the product of xi fi given by 5 multiplied by 10, 50, 20 multiplied by 10, 200, 30 multiplied by 6, 180, 40 multiplied by 10, 400. Now summation xi fi is equal to 50 plus 200 plus 180 plus 400 and this comes out to be equal to 8, 30, then summation fi is equal to 5 plus 10 plus 6 plus 10 equal to 31. Now mean is equal to summation xi fi upon summation fi that is equal to 8, 30 upon 31. This is equal to 26.77. Now the total frequency n is equal to summation fi is equal to 31 which is odd. Now from the key idea you can see that when n that is the total frequency is odd then median is equal to the size of n plus 1 upon 2th item. So here we have median is equal to the size of n plus 1 upon 2th item that is equal to the size of 31 plus 1 upon 2th item which is equal to the size of 16th item. Or we can also say this is equal to the daily wage earned by the 16th worker. Now from the table you can see that the cumulative frequency 16 is less than 21. So daily wage earned by the 16th worker would be given by 30. So we get that the median is equal to 30. So we have now got the mean equal to 26.77 and median is equal to 30. Now the empirical formula for mode is given by mode is equal to 3 times median minus 2 times the mean. So this is equal to 3 multiplied by median which is 30 minus 2 multiplied by mean which is 26.77. So this is equal to 90 minus 53.54 and 90 minus 53.54 is equal to 36.46. So we get the mode is equal to 36.46. Now our final answer is mean equal to 26.77, median equal to 30 and mode is equal to 36.46. So this completes the session. Hope you have understood the solution for this question.