 Hello and welcome to the session. In this session we discussed the following question which says, the main and standard deviation of monthly salary in dollars are given below the factories A, B and C, find the combined main and combined standard deviation. Before we move on to the solution, let's discuss the formula for the combined main and combined standard deviation. First we have the combined main denoted by x bar is equal to m1 x1 bar plus m2 x2 bar this whole upon m1 plus m2. If we have the formula for the combined standard deviation denoted by sigma or sigma12 when we have 2 series 1 and 2 and so this would be equal to square root s m1 into sigma1 square plus t1 square the whole into into t2 square the whole and this whole upon m1 plus m2 under deviation and here we have 2 series where this m1 x1 bar is the arithmetic name of the series 1 sigma1 deviation series 1 is equal to x1 bar minus x bar where this x bar is the combined main when we have for the series 2 is the size of the series of the series deviation of the series 2 is equal to x2 bar minus x bar key idea that we use for this question. Let's now proceed with the solution. We are given this table in which we have 3 factories A, B and C their respective number of employees their average monthly salaries in dollars and their respective standard deviations and we are supposed to find the combined main and the combined standard deviation The factories A, B and C this means we have 3 series so m1 would be the size of series 1 that is which means that the number of employees in factory A that is 50 so m1 is equal to 50 the average monthly salary is the arithmetic name which is the average monthly salary for factory A and this is equal to 61 under deviation for the factory A and this is factory B that is the number of employees in factory B which is 100 monthly salary for factory B which is 70 patient for factory B which is 9 next for factory C m3 is 120 80.5 The combined main denoted by x bar and this would be equal to m1 x1 bar plus m2 x2 bar m3 is equal to that is m1 is 50 x1 bar is 61 plus x2 bar that is m2 plus m3 that is 50 plus 100 plus 120 that is equal to 7000 6 0 and this whole term this is equal to 2 cancels with 0 9 3 times is 27 27 3 times is 1971 then 9 57 is equal to 73 mind mean is 73 s sigma and this would be equal to 2 square v 0 plus 3 square plus and this whole term so we combine standard deviation that is single d1 d2 and d3 is equal to x1 bar minus x bar which is 73 this is equal to minus 12 that is we have d1 equal to minus 12 then d2 is equal to x2 bar which is equal to 70 minus 73 and that is equal to minus 3 d2 equal to like this d3 this is equal to x3 bar minus x bar which is equal to 80.23 and this is equal to 7.5 3 is equal to 7 point put the values in the combined standard deviation formula we would have the combined standard deviation sigma is equal to square plus d1 square the whole now the value of 1 square that is 8 square which is 64 plus d1 square which would be minus 12 square and that is 144 plus so into sigma 2 square plus d2 square the whole point square which is 81 plus d2 square and d2 is minus 3 so minus 3 square is 9 3 is 120 so 123 square that is 10 square which is 100 d3 square that is 7.2 is equal to d1 plus 9 which is 90 120 into 6.25 and this whole appell 50 and this whole appell which is equal to and this is with 0 15 appell 27 which is equal to 1.30 and this square root is equal to 11.89 that is we get sigma is equal to 11.89 standard deviation thus x bar is equal to 73 given by sigma is equal to 11.89 we have understood the solution of this question