 Hello and welcome to the session. In this session we discuss the following question which says find the mean of 20 numbers if the mean of 15 of them is 20 and the mean of the remaining numbers is 10. Before we move on to the solution let's recall what is mean. It is denoted by x bar and this is equal to summation xi i goes from 1 to n upon n that is mean is found by adding all the values of the observations and dividing it by the total number of observations. This is the key idea to be used in this question. Now we move on to the solution. In the question we are given that the mean of 15 numbers is equal to 20. So this means that 20 is equal to summation xi i goes from 1 to 15 upon 15. That is we have substituted the value for x bar and n in the formula for the mean. So this gives us summation xi i goes from 1 to 15 is equal to 20 into 15 and this is equal to 300. This means that the sum of the 15 numbers is equal to 300. Now it is given that the total number are 20 numbers and the mean of the remaining numbers that is 20 minus 15 that is 5 numbers is 10. So the mean of the 5 numbers is equal to 10 this means that 10 is equal to summation xi i goes from 1 to 5 upon 5. So this gives us summation xi i goes from 1 to 5 is equal to 10 into 5 equal to 15. That is we have got the sum of the remaining 5 numbers is 15. Now the sum of 15 numbers is 300 and sum of the remaining 5 numbers is 50. So we can say that the sum of the total 20 numbers given to us is equal to the sum of the 15 numbers that is 300 plus the sum of the remaining 5 numbers that is 50 is equal to 350. Now that we have got the sum of 20 numbers as 350 we can easily find out the mean of the 20 numbers. This is given by sum of 20 numbers that is 350 divided by 20 that is the total numbers given to us and this comes out to be equal to 17.5. So this is our final answer that is mean of 20 numbers is 17.5. This completes the session. Hope you have understood the solution for this question.