 Hi and welcome to the session where we discuss the following question the question says find the mean deviation about the mean for the data and exercises 526 this is the data given to us and we have to find the mean deviation about the mean of this data. Now before solving this question we should note the steps which are involved in the calculation of mean deviation about the of a discrete frequency distribution. In the first step we find the mean of the given data by using the formula mean is equal to 1 by n into summation i varying from 1 to n pi x i where n is equal to summation i varying from 1 to n pi. In the second step we find the deviation of each x i from x bar that is x 1 minus x bar x 2 minus x bar so on x n minus x bar. In the third step we find the absolute value of each deviation that is drop the minus sign if it is there that is mod of x 1 minus x bar x 2 minus x bar in mod and so on. And in the last step find the mean of the absolute values of the deviations this mean is the mean deviation about mean that is mean deviation about mean is equal to 1 by n into summation i varying from 1 to n pi into mod x i minus x bar where n is equal to summation i varying from 1 to n pi. Always remember these steps we will be using this step for solving this question. So now begin with the solution we will first make a table in the first two columns we have written the given data. Now in this column we will find the product of f i and x i. In the first row x i is 10 and f i is 4 so we have 10 into 4 and 10 into 4 is 40. In the second row we have 30 into 24 30 into 24 is 720 then 15 to 28 is 1400 then 70 into 16 is 1120 and then 90 into 8 is 720. To first find n, n is equal to summation i varying from 1 to n. Now here n is 5 as the number of observations is 5 f i. Now this is equal to 4 plus 24 plus 28 plus 60 plus 8 on adding all these frequencies we get 80. Now we will find summation i varying from 1 to 5 f i x i this is equal to 40 plus 720 plus 1400 plus 1120 plus 720 this is equal to 4000. Going to calculate mean that is x bar. x bar is equal to 1 by n summation i varying from 1 to 5 f i x i. By substituting values we get 1 by 80 into 4000 and this is equal to 50. So mean of the given data is 50. Now we will find x i minus x bar. x bar is equal to 50 and in the first row x i is equal to 10 so we have 10 minus 50 and 10 minus 50 is minus 40. Then we have 30 minus 50, 30 minus 50 is minus 20, 50 minus 50 is 0, 70 minus 50 is 20, 90 minus 50 is 40. Now we will find mod of x i minus x bar absolute value of minus 40 is 40, absolute value of minus 20 is 20 and absolute value of 0, 20 and 40 is 0, 20 and 40. We will find f i into mod x i minus x bar. In the first row f i is 4 and mod of x i minus x bar is 40 so we have 4 into 40, 4 into 40 is 160, 24 into 20 is 480, 28 into 0 is 0, 16 into 20 is 320, 8 into 40 is 320. So summation by varying from 1 to 5 f i into mod x i minus x bar is equal to 160 plus 480 plus 0 plus 320 plus 320 and this is equal to 1280. So on adding this we get 1280 and we have already calculated that some of all these frequencies is 80. And summation i varying from 1 to 5 f i x i is 4000. We need to calculate mean deviation about mean that is x bar. Now mean deviation about x bar is equal to 1 by n into summation i varying from 1 to 5 f i into mod x i minus x bar. By substituting values we get 1 by 80 into 1280 and this is equal to 16. Hence a required answer is 16. So this completes the by nj care.