 Hello and welcome to the session. In this session we discussed the following question which says that the mean of 80 items was found to be 60. Later on it was discovered that two items were misread as 25 and 6 instead of 35 and 16 respectively. Find the correct mean. Before moving 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 for this question. Now let's see the solution. Now the mean of 80 items is 60 that is you can say that we are given x bar is equal to 60 and n is equal to 80 that is we have 60 is equal to summation xi i goes from 1 to 80 upon 80 that is substituting the values for x bar and n in the formula for the mean. So this gives us summation xi i goes from 1 to 80 is equal to 60 into 80 that is equal to 4800. This means that the sum of 80 items is equal to 4800 but as given the question two items were misread as 25 and 6 that is instead of 35 the person read the number as 25 and instead of 16 the person read the number as 6. So there would be some correction in the sum of 80 items. So now we will find out the correct sum of 80 items and this would be given by the sum of 80 items calculated that is 4800 minus the sum of wrong items plus the sum of correct items. Now the wrong items are 25 and 6 and so this would be equal to 4800 minus 25 plus 6 that is the sum of wrong items plus the sum of the correct items which are 35 and 16. So this is further equal to 4800 minus 31 plus 51 this is equal to 4800 plus 20 which is equal to 4820. 4820 is the correct sum of 80 items. Now the correct mean of the 80 items would be equal to the correct sum of 80 items upon the total number of items that is 80. Now we have got the correct sum of 80 items as 4820 upon 80. Now 0 and 0 cancels and this comes out to be equal to 60.25. So 60.25 is the correct mean of 80 items. So this is the final answer. This completes the session. Hope you have understood the solution for this question.