 Hi and welcome to the session. Let us discuss the following question. The question says, find the mean deviation about the median for the data in exercises seven and eight. This is the data given to us. Now before solving this question, we should note the steps which are involved in the calculation of mean deviation about median of a discrete frequency distribution. In the first step, we arrange the observation that is xi's in ascending order. After this, we calculate the cumulative frequency and then we calculate n equals to summation i goes from 1 to n if i. If n is odd, then the median is that xi observation whose cumulative frequency is equal to or just greater than n plus 1 by 2th observation. If n is even, then first we take xi observations whose cumulative frequency is equal to or greater than n by 2th observation and n by 2 plus 1th observation. Then median is sum of both xi's divided by 2. Now let median is equal to capital N. In the second step, we will find deviation of each xi from n that is x1 minus m x2 minus m so on xn minus n. 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 x1 minus m mod x2 minus m so on mod xn minus m. And in the last step, find the mean of the absolute values of the deviation. This mean is the mean deviation about median that is mean deviation about median is equal to 1 by n into summation i goes from 1 to n, f i into mod xi minus m where n is equal to summation i goes from 1 to n f i and m is equal to median of the given data. So keeping all these steps in mind, let's now begin with the solution. We will first make a table from the given data. First, we will arrange the xi's in ascending order. Now here the xi's are already in ascending order. So we have 5, 7, 9, 10, 12 and 15 in this column. And now in this column, we will write its corresponding frequency. So we have 8, 6, 2, 2, 2, 6. Now we will calculate cumulative frequency of f i. In the first row, we will write a. In the second row, we will write 8 plus 6 that is 40. In the third row, we will write 8 plus 6 plus 2 that is 16. In the fourth row, we will write 16 plus 2 that is 80. In the fifth row, we will write 18 plus 2 that is 20. And in the sixth row, we will write 20 plus 6 that is 26. Find n, n is equal to summation i goes from 1 to 6 f i and this is equal to 8 plus 6 plus 2 plus 2 plus 2 plus 6 and this is equal to 26. Now 26 is even and we know that if n is even, then first we take xi's observation whose cumulative frequency is equal to or just greater than n by 2 at observation and n by 2 plus 1 at observation. And then we find the media equal to sum of both xi's by 2. Now n is equal to 26 so n by 2 is equal to 26 by 2 and this is equal to 30 and n by 2 plus 1 is equal to 40. So we have to take those xi's whose cumulative frequency is greater than or equal to 13 and 14. Now look at the table, only 7 is the observation whose cumulative frequency is just greater than 13. So we will take xi's as 7 and 7. Now we will find media, median is equal to 7 plus 7 by 2 and this is equal to 7. The median of the given data is 7. Now we will find xi minus n. Now n is equal to 7 value of xi in the first row is 5. So we have 5 minus 7 and 5 minus 7 is minus 2. Then we have 7 minus 7, 7 minus 7 is 0, 9 minus 7 is 2, n minus 7 is 3, 12 minus 7 is 5, 15 minus 7 is 8. Now we will find mod of xi minus m. Absolute value of minus 2 is 0, absolute value of 0, 2, 3, 5 and 8 is 0, 2, 3, 5, 8. Now we will find fi into mod xi minus m. In the first row, value of fi is 8 and value of mod xi minus m is 2. So we have 8 into 2 and 8 into 2 is 16. Then we have 6 into 0, 2 into 2 is 4, 2 into 3 is 6, 2 into 5 is 10, 6 into 8 is 48. Adding all this, we get a4. So summation i goes from 1 to 6 fi into mod xi minus m is equal to 84. Now we will calculate mean deviation about median. Now mean deviation about median is equal to 1 by n into summation i goes from 1 to 6 fi into mod xi minus m. n is equal to 26 and summation i goes from 1 to 6 fi mod xi minus m is 84. So we have 1 by 26 into 84 and this is equal to 3.23. Hence our required answer is 3.23. So this completes the session. Bye and take care.