 Hello and welcome to the session. In this session we discussed the following question which says, if the mean of the following frequency distribution is 6, find the value of p. This is the frequency distribution given to us in which we have the variable xi and frequency fi. Before we move on to the solution, let's recall the formula to calculate the mean. We take let the frequencies of n observations x1, x2 and so on up to xn be f1, f2 and so on up to fn respectively then the mean is equal to summation fi xi where we have i goes from 1 to n upon summation fi where i goes from 1 to n. This is the key idea to be used for this question. Now we move on to the solution. To calculate the mean we need to make a table. In this table we have the variable xi, the corresponding frequency is fi and the product of the variable xi and frequency fi. We are given the variable xi as 3, 2, 4, 5, 7. Now the frequency fi for variable xi when xi is 3 is 2. When xi is 2, frequency is 3. When xi is 4, frequency is 4. When xi is 5, frequency is 5. When xi is 7, frequency is p. Now the product of fi and xi is 6, 6, 16, 25, 7, p. Then we have summation fi is equal to the sum of the subverse that is 2 plus 3 plus 4 plus 5 plus p and this is equal to 14 plus p. Then summation fi xi is equal to the sum of these numbers that is equal to 6 plus 6 plus 16 plus 25 plus 7p and this is equal to 53 plus 7p. Now mean is equal to summation fi xi upon summation fi that is equal to 53 plus 7p upon 14 plus p. In the question we are given that the mean of the frequency distribution is 6. So we have 53 plus 7p upon 14 plus p is equal to 6 since we are given the mean equal to 6. So this gives us 53 plus 7p is equal to 6 multiplied by 14 plus p that is 53 plus 7p is equal to 84 plus 6p. This gives us 7p minus 6p is equal to 84 minus 53 that is we have p is equal to 31. We were supposed to find the value of p which is equal to 31. So our final answer is p equal to 31. This completes the session. Hope you have understood the solution for this question.