 Hello and welcome to the session. Let us discuss the following question, question says, consider the following distribution of daily wages of 50 workers of a factory. Find the mean daily wages of the workers of the factory by using an appropriate method. This is the given table. First of all let us understand that according to assumed mean method mean is equal to a plus summation fi di upon summation fi. Now in this formula x bar is mean a is assumed mean fi is frequency di is the deviation of a from each of the xi. Or we can say it is deviation of assumed mean from class mark we know xi is class mark. This is the key idea to solve the given question. Let us now start with the solution. First of all we will rewrite the data given in the question. We are given daily wages of workers in rupees and number of workers. Now we know number of workers represent f1 that is frequency. Now we will find out class mark for every class interval. We know xi represents class mark. Now class mark is equal to upper class limit plus lower class limit upon 2. So 120 plus 100 upon 2 is equal to 110. Similarly 140 plus 120 divided by 2 is equal to 130. Now class mark for this interval is equal to 150. Similarly class mark for this interval is equal to 170 and for this interval class mark is equal to 190. Now we will choose one among the xi's as the assumed mean. Let it be 110. So we will denote it by a. So we can write assumed mean that is a is equal to 110. Now we will find out di. We know di is equal to xi minus a. Di represents deviation of assumed mean from xi that is class mark. So we know here for first class interval xi is equal to 110 and a is also equal to 110. So deviation is equal to 0. Similarly here xi is equal to 130 and a is equal to 110. So 130 minus 110 is equal to 20. Similarly 150 minus 110 is equal to 40. 170 minus 110 is equal to 60. 190 minus 110 is equal to 80. Now we will find out the product fi di. We know 12 multiplied by 0 is equal to 0. 14 multiplied by 20 is equal to 280. 8 multiplied by 40 is equal to 320. 6 multiplied by 60 is equal to 360 and 10 multiplied by 80 is equal to 800. Now we will find out summation fi. We know summation fi is equal to sum of all the frequencies. So it is equal to 50. Now we will find summation fi di. We know summation fi di is equal to sum of all these products. So it is equal to 1760. From key idea we know mean is equal to assumed mean plus summation fi di upon summation fi. In this formula x bar is the mean, a is the assumed mean, fi is the frequency, di is the deviation of assumed mean from xi. Now substituting corresponding values of a summation fi di and summation fi in this formula we get x bar is equal to 110 plus 1760 upon 50. Now simplifying we get x bar is equal to 110 plus 35.2. Now adding these two terms we get mean is equal to 145.2. So we get mean daily wages of the workers of the factory is equal to rupees 145.2. Always remember that assumed mean method is used when the numerical values of xi and fi are large. So our required answer is rupees 145.20. This completes the session. Hope you understood the solution. Take care and have a nice day.