 Hello and how are you all today the question says find the mean and variance for the data now here the X, Y and F, I are given to us and we need to find out the mean as well as variance now as we are well first with their formulas let us start with our solution now let us form a table to simplify our question now this is the table that that we have drawn over here now first of all to find out the mean we need to find out X, I, F, I that means we need to multiply X, I with F, that is 92 with 3 giving us the answer as 276 then 93 with 2 giving us 186, 97 with 3 giving us 291 then we need to multiply 98 with 2 which will give us 196 and so on we have 612 as the product 312 has a product of 104 and 3 and 327 now finding out the sum on finding out the sum it is coming out to be 2200 and finding the sum of X sorry F, I we have 22 so before proceeding on to the next step since we need to need to find the value of mean and then only we can proceed on with the next step let us find out the mean so we have mean is equal to 1 upon n summation F, I, X, I where I is equal to 1 till n that is on substituting the value 2200 divided by 22 giving us the answer on simplification as 100 so we have mean equal to 100 now let us proceed on with the next step now here in the next step we need to subtract the mean that is 100 from each X, I and on doing so we have 92 minus 100 giving us minus 8, 93 minus 100 minus 7 then minus 3 minus 2 2 4 and 9 now what we need to do is we need to square them and their square is 64 49 94 again 4 then we have 16 and the square of 9 is 81 now we need to multiply with F so we need to multiply 3 with 64 and we have 192 on doing that 2 with 49 we have 98 and so on 3 into 9 27 2 into 4 8 6 into 4 24 3 into 16 48 and 3 into 81 is found out to be 243 now to find out the variance firstly we need to sum them up so their sum is coming out to be 640 so we have further variance equal to 1 upon n sigma Fi into Xi minus mean the whole square where I is equal to 1 till n let us substitute the value so we have 1 upon n that is 22 into the sum which we have found out above as 640 so it will get multiplied by 640 on simplifying we have the answer as 29.09 we can summarize the answer and can write that we found out mean is equal to 100 and variance is equal to 29.09 right so this ends my session hope you understood the whole concept well do make your table very neat and clear so as to avoid any calculation error so have a nice day bye for now