 Hi and how are you all today? My name is Priyanka and let us discuss this question. It says find the missing frequency in the following table. Mean is given to us as 50 and total frequency is given to us as 20. These are the class intervals and the corresponding frequencies which are given to us. Now let us proceed with our solution. Let us make a table. Now here with the help of these class intervals and the frequency we will first find out xi that is the midpoint of this class interval that is 0 plus 20 divided by 2 that gives us 10, 20 plus 40 divided by 2 gives us 30 and so on with the difference of 20 we will write down all the xi's. Now we will find ui that is xi minus 50 that is the mean which is given to us in the question and that we will divide by h which will be the common factor of all ui's that is 10 minus 50 will give us minus 40 minus 40 divided by 20 will give us minus 2 so that means here h is 20. Now 30 minus 50 that is minus 20 divided by 20 gives us minus 1 and so on. We will find all the ui's. Now we will multiply f with ui to give us fi ui and that is 17 into minus 2 minus 34 fi into minus 1 gives us minus f sorry f1 f1 into minus 1 minus f1 32 into 0 0 f2 into 1 gives us f2 19 into 2 gives us 38. Now the sum of all these frequencies are equal to 68 plus f1 plus f2 and here we have summation fi ui equal to 4 minus f1 plus f2 but in the question we are given that the sum of all the frequencies is equal to 120 right. So here we will equate it to 120 which will help us to find out the sum of f1 and f2 that is 120 minus 68 that is equal to 50 to let this be the first equation further. We can find the mean by using this shortcut method that is given to us as 50 plus that is the mean plus h that is 20 which we took here divided ui by h every time into summation fi ui divided by total number of frequencies that is 120. This implies mean is equal to 50 plus 4 minus f1 plus f2 upon 6. This implies we are given mean as 50 let us substitute it so 50 is equal to 50 plus 4 minus fi plus f1 plus f2 upon 6 which is equal to 4 minus f1 plus f2 upon 6 is equal to 0 which further gives us 4 minus f1 plus f2 is equal to 0 which is f1 minus f2 is equal to 4 let this be the second equation. Now the two equations that we have are f1 plus f2 is equal to 52 and f1 minus f2 is equal to 4. Now on adding these two equations these two will get cancelled out we have 2f1 is equal to 50 6 that implies f1 is equal to 56 divided by 2 that is 28 if f1 is 28 then f2 will be equal to 24 so the answer to the session is f1 is equal to 28 and f2 is equal to 24 right so this completes the solution hope you understood it well enjoy it to have a nice day ahead.