 Hi, and welcome to our session. Let us discuss the following question. The question says, find the mean deviation about the mean for the data in exercises 1 and 2. This is the data given to us. Before solving this question, we should know that what is meant by an deviation of an observation 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. So always remember, by deviation of an observation x from a fixed value a, we mean the difference between x and a, that is, x minus a. Now we are going to learn the steps which are involved in the calculation of mean deviation about mean. Let n observations be x1, x2, x3, so on, xn. In the first step, we find the mean of the observations using formula, x bar is equal to sum of observations divided by number of observations, that is, x1 plus x to so on plus xn upon a. Now let a is equal to x bar. In the second step, we find the deviation of each xi from a, that is, x1 minus a, x2 minus a, so on, up to xn minus a. Then in the third step, we find the absolute values of each deviation, that is, drop the negative sign if it is there. That means we have to find mod of xi minus a. Then in the last step, we find the mean of the absolute values of the deviations. And this mean is the mean deviation about a, that is, mean deviation about me is equal to 1 by n into summation i varying from 1 to a, mod of xi minus a. So always remember these steps. Let's now begin with the solution. In the first step, we will calculate mean of the given data. Now mean of the given data, that is, x bar is equal to sum of the observation status, 38 plus 70 plus 48 plus 40 plus 42 plus 55 plus 63 plus 46 plus 54 plus 44 divided by number of observation status 10. Now this is equal to 500 by 10. And this is equal to 15. So mean of the given data is 15. In the second step, we will find deviation of each observation from the mean x bar. That means we will now find xi minus x bar. Now the first observation is 38. So x1 minus x bar is equal to 38 minus 50. And this is equal to minus 12. Second observation is 70. So we have 70 minus 50. This is equal to 20. Third observation is 48. So we have 48 minus 50. This is equal to minus 2. Fourth observation is 30. So we have 40 minus 50. And this is equal to minus 10. Then the fifth observation is 42. So x5 minus x bar is equal to 42 minus 50. And this is equal to minus 8. Then we have 55 minus 50. This is equal to 5. Then we have 63 minus 50. This is equal to 30. Then we have 46 minus 50. This is equal to minus 4. Then we have 54 minus 50. This is equal to 4. And the last observation is 44. So we have 44 minus 50. And this is equal to minus 6. Third step, we will find absolute value of each deviation. So that means we will now drop the minus sign if it is there for each deviation. The first deviation is minus 12. We have a minus sign there. So we will now drop this minus sign. So we have 12. Then we have 20. Then we have minus 2. Absolute value of minus 2 is 2. Then we have minus 10. Absolute value of minus 10 is 10. Then we have minus 8. Absolute value of minus 8 is 8. Then we have 5, 30. Absolute value of minus 4 is 4. Then we have 4. Absolute value of minus 6 is 6. Now, in the last step, we will calculate mean deviation about me. The mean deviation about me is equal to 1 by n into summation i varying from 1 to n of xi minus a. Summation mod xi minus a is equal to sum of the absolute values of deviations. This is equal to 12 plus 20 plus 2 plus 10 plus 8 plus 5 plus 30 plus 4 plus 4 plus 6 divided by number of observations that is 10. Now, this is equal to 84 by 10 and this is equal to 8.4. Hence the required mean deviation about me is 8.4. This is our required answer. So, this completes the session. Bye and take care.