 and welcome to the session. Let us discuss the following question. The question says, find a mean deviation above the me for the data in exercises 5 and 6. This is the data given to us. Before solving this question, we should know that what is meant by deviation of an observation x from a fixed value a. By deviation of an observation x from a fixed value a, we mean the difference between x and a, that is, x minus a. Observations are the given values which we call as x1, x2, x3, so on, xn. Now we are going to learn the steps which are involved in the calculation of mean deviation about mean of a discrete frequency distribution. In first step, we find the mean of the given data by using the formula x bar is equal to 1 by n into summation i waiting from 1 to n fi xi, where n is equal to summation i waiting from 1 to n fi. In the second step, we find the deviation of each xi from x bar, that is, x1 minus x bar, x2 minus x bar, so on, xn minus x bar. Absolute value of each deviation, that is, drop the negative sign if it is there, that is, mod of x1 minus x bar, mod of x2 minus x bar, so on, mod of xn minus x bar. 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 waiting from 1 to n fi into mod of xi minus x bar, where n is equal to summation i waiting from 1 to n fi. Remember, these steps, we will be using these steps for solving this question. In the first two columns of this table, i xi, since we need this for calculated mean. In the first, the value of fi is 7, so we have 5 into 7 and 5 into 7 is 35. Then, we have into 4 is 40, then we have 15 into 6, 15 into 6 is 90, then we have 20 into 3, 20 into 3 is 60 and at last we have 25 into 5 and this is 125. We know that mean is equal to 1 by n into summation i waiting from 1 to n fi xi, where n is equal to summation i waiting from 1 to n fi. So, let's first calculate n, the two summation i waiting from 1 to n. Now, here n is 5 as the number of observations is 5 is equal to 25. So, sum of all these frequencies is find summation i waiting from 1 to 5 equal to 35 plus 40 plus 90 plus 60 plus 125 and this is equal to 350. So, sum of all this 350. So, mean of the given data that is x power is equal to 1 by n into summation from 1 to 5 substitute both the values. This is equal to 1 by 25 into 350 and this is equal to 40. The mean of the given data is 14 find xi minus x power. First row xi is 5, so we have 5 minus 40 and 5 minus 14 is minus 9, then we have 10 minus 14, 10 minus 14 is minus 4, then we have 15 minus 14, 15 minus 14 is 1, 20 minus 14 is 6, 25 minus 14 is 11. Now, we will find mod of xi minus x power. Absolute value of minus 9 is 9, absolute value of minus 4 is 4 and absolute value of 1, 6 and 11 is 1, 6 and 11. Now, in the last column we will find fi into mod of xi minus x power. In the first row fi is 7 and mod of xi minus x power is 9, so we have 7 into 9, 7 into 9 is 63, then we have 4 into 4, 4 into 4 is 16, then we have 6 into 1, 6 into 1 is 6, then we have 3 into 6, 3 into 6 is 18, then we have 5 into 11 and 5 into 11 is 55. On adding all this, we get 158. So, summation from 1 to 5 fi into mod xi minus x power is 158. Now, required mean deviation about mean is equal to 1 by n into summation i varying from 1 to 5 fi into mod xi minus x power. This is equal to 1 by 25 into 158, this is equal to 6.32. Hence, our required answer is 6.32. So, this completes the session. Bye and take care.