 Hi, and welcome to the illustration. Let us discuss the following question. The question says, find the mean deviation about the mean for the data in exercises 1 and 2. Given data is 4, 7, 8, 9, 10, 12, 13, 17. Before solving this question, we should know that what is meant by an deviation. By deviation of an observation x from a fixed value a, we mean the difference between x and a. That is, x minus going to learn the steps which are involved in the calculation of mean deviation about the 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 equals to sum of observations divided by number of observations. That is, x1 plus x2, so on, plus x1 divided by a. Now, let a is equal to x bar. In the second step, we find the deviation of each xi from a. That means we will find x1 minus a, x2 minus a, and so on, xn minus a. Now, in the third step, we find the absolute values of each deviation. That is, drop the minus sign if it is there. Or we can say that we have to find the absolute value of xi minus a. Then in the last step, we find the mean of the absolute values of the deviation. And this mean is the mean deviation about a. That is, mean deviation about mean is equal to 1 by n into summation i varying from 1 to n, mod xi minus a. So, always remember these steps. Giving all this in mind, let's now begin with the solution. In step one, we will calculate the mean of the given data by using the formula. Mean is equal to sum of the observations divided by number of observations. So, mean, which we denote by x bar, is equal to... Now, here the observations are 4, 7, 8, 9, 10, 12, 13, 17. So, their sum is 4 plus 7 plus 8 plus 9 plus 10 plus 12 plus 13 plus 17. And number of the observations is 8. So, we will divide this by 8. And this is equal to... On adding all this, we get 80. So, we have 80 by a. And this is equal to 10. So, mean of the given data is 10. Second step, find deviation each observation in the mean x bar. That means we have to now find xi minus x bar. Now, the first observation is 4. So, we have 4 minus 10. This is equal to minus 6. Second observation is 7. So, we have 7 minus 10. This is equal to minus 3. Then we have 8 minus 10. This is equal to minus 2. Then we have 9 minus 10. This is equal to minus 1. Then we have 10 minus 10. It is equal to 0. Then we have 12 minus 10. This is equal to 2. Then we have 30 minus 10, this is equal to 3 and the last one observation is 17, so we have 17 minus 10 and this is equal to 7. So in the second step we have calculated deviation of each observation from the v x bar. We will find absolute value of each deviation. That means we will now drop the minus sign if it is there with each deviation. The first deviation which we have calculated is minus 6. So absolute value of minus 6 is 6, then we have minus 3. Absolute value of minus 3 is 3, then we have minus 2. Absolute value of minus 2 is 2, then we have minus 1. Absolute value of minus 1. Absolute value of 0 is 0, absolute value of 2 is 2, absolute value of 3 is 3 and absolute value of 7 is 7. In the last step we will find mean deviation about x bar. Mean deviation about x bar is equal to 1 by n into summation i varying from 1 to n. Mod of x i minus a is plus 1 plus 0 plus 2 plus 3 plus 7. Number of the observations are 8, so we will divide this by 8. Now this is equal to 24 by a and this is equal to 3. Hence the required mean deviation about mean is, this is our required answer. So this completes the session. Bye and take care.