 Hello and welcome to the session. In this session we will discuss a problem on corrected mean which says that the mean of 100 items is 80, but by mistake one item is misread as 33 instead of 88. Find the correct mean. In the question we are given 100 items with the mean value as 80, but by mistake one item which was actually 88 misread as 33. Now we have to find the correct mean value. Now we know that the mean of a set of numbers x1, x2 and so on up to xn is defined as x bar given by x1 plus x2 plus and so on up to xn whole divided by n or we can write x bar as summation xi where i goes from 1 to n whole divided by n and n is equal to the number of elements in the set. So we can say that the mean of a set of numbers x1, x2 up to xn is given by the formula x bar which is equal to submission xi where i goes from 1 to n whole divided by n. This is the key idea we shall be using in this question. Now moving on to the solution in the question we have 100 items in all and the mean value of these 100 items is given as 80. Here we have the number of items denoted by n is equal to 100 and the mean value of these 100 items denoted by x bar is given as 80 by using the key idea we know that the mean of a set of numbers x1, x2 up to xn is given by x bar equal to submission xi where i goes from 1 to n whole divided by n. Using the same formula to calculate the mean we have x bar equal to submission x divided by n or on putting the values of x bar and n we get 80 equal to submission x divided by 100 or we can write 80 multiplied by 100 is equal to submission x which gives the value of submission x as 8000 but this value submission x is incorrect 88 was misread as 33 therefore correct value of submission x is given by incorrect value of submission x minus incorrect item value plus correct item value. Now we know the incorrect submission x value is 8000 the incorrect item value is 33 and the correct item value is 88 therefore on putting the required values we get 8000 minus 33 plus 88 which gives 8055. Now we have got the correct submission x value as 8055. Now we can find the correct mean by using the key idea which states that the mean of a set of numbers is given by the formula x bar equal to submission xi where i goes from 1 to n divided by n. Therefore we get correct mean equal to submission x whole divided by n. Now our new submission x value is 8055 that is 8055 and value of n is 100. So the value of correct mean is equal to 80 decimal 55. Therefore the value of correct mean is given by 80 decimal 55 which is our final answer. This completes the session hope you have understood it well.