 Hello and how are you all doing today? The question says the arithmetic mean of the following frequency distribution is 47. Determine the value of P. Here we are given the classes as 0 to 20, 20 to 40, 40 to 60, 60 to 80 and 80 to 100 and their respective frequencies are 8, 15, 20, P, 5. We need to find out the value of this P. So let us proceed with the solution. Let us redraw the given table once again. Now here let us first find out x i that is the midpoint of, that is the class mark let us say of these classes, that is 10, 30, 50, 70 and 90. That is 80 plus 100 upon 2. In each and every case we will add the lower limit to the upper limit and divide the sum by 2. Now we will multiply x i with x i to get 80, 450,000, 70 P and we have 450 again. Now here we will find out the sum of f i and the sum of f i x i. That is, and here it is coming out to be 1980 plus 70 P. We know that the formula for arithmetic mean is equal to summation f i x i divided by summation f i. That is further equal to, now here mean is given to us in the question as 47. So we have 47 equal to 1980 plus 70 P divided by 48 plus P, which on simplifying will give us 47 into 48 plus P equal to 1980 plus 70 P. That further equal to 2256 plus 47 P equal to 1980 plus 70 P. Now we are solving for P. Now we have 2256 minus 1980 equal to 70 P minus 47 P. That is equal to, that further implies that the value for P is equal to 276 divided by 23, quotient is coming out to be. So this is the answer to the given question. So this completes the session. Hope you understood it and enjoyed it too. Have a nice day.