 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that calculate the mean deviation and its coefficient from the mean for the following data. Where the size of items is given as 3 to 4, 4 to 5, 5 to 6, 6 to 7, 7 to 8, 8 to 9 and 9 to 10 with the corresponding frequency as 3, 7, 22, 60, 85, 32 and 8. We know that the mean deviation from the mean can be calculated using the formula summation of f into modulus of x minus x bar whole upon m where x bar which is called mean is given by summation of f into x upon summation of f. Also the coefficient of mean deviation is given by the formula that is mean deviation from the mean with this key idea let us proceed with the solution. Now we are given the following distribution of data where the size of the items with the corresponding frequencies are given then x series is given by taking mean of each of the 5 of the items then for the size 3 to 4 we take 3.5, for 4 to 5 we take 4.5, for 5 to 6 we take 5.5, for 6 to 7 we take 6.5, for size 7 to 8 we take 7.5, for the size 8 to 9 we take 8.5, for size 9 to 10 we take 9.5, Now we should find the series for f into x modulus of x minus x bar and f into modulus of x minus x bar. Now f into x series is given by 3.5 into 3 that is 10.5, 4.5 into 7 that is 21.5, 5.5 into 22 that is 121, 6.5 into 60 that is 390, 7.5 into 85 that is 637.5, 8.5 into 32 that is 27.5, and 9.5 into 8 that is 76. And from the key idea we know that the mean that is x bar is given by the formula summation of f into x upon summation of f. Therefore mean that is x bar is given by summation of f into x upon summation of f. Now summation of f that is sum of all the entries in the frequency series is equal to 217, and summation of f into x that is sum of all the entries in the f into x series is given by 1538.5. Therefore mean x bar is equal to summation of f into x that is 1538.5 upon 217 which is equal to 7.09. Therefore x bar is equal to 7.09. Now the value of x bar is given by 7.09. Therefore modulus of x minus x bar series is given by modulus of 3.5 minus 7.09 which is equal to 3.59. Modulus of 4.5 minus 7.09 which is equal to 2.59. Modulus of 5.5 minus 7.09 which is equal to 1.59. Modulus of 6.5 minus 7.09 which is equal to 0.5. Next is modulus of 7.5 minus 7.09 which is equal to 0.41. Next is modulus of 8.5 minus 7.09 which is equal to 1.41. Then we have modulus of 9.5 minus 7.09 which is equal to 2.41 and then we find out S into modulus of X minus X bar series which is given as S into modulus of X minus X bar that is 3 into 3.59 which is equal to 10.77. Next is 7 into 2.59 that is 18.13. Then 22 into 1.59 that is 34.98. Then we have 60 into 0.59 that is 35.40. Next is 35 into 0.41 that is equal to 34.85. Then we have 32 into 1.41 which is equal to 45.12 and then 8 into 2.41 that is 19.28. And the value of summation of S into modulus of X minus X bar is equal to 198.53. Now we need to find the mean deviation from the mean which is given by the formula. Summation of S into modulus of X minus X bar whole upon N. Therefore mean deviation from mean is given by summation of S into modulus of S minus X bar by N. Where N is equal to some of the frequencies denoted by summation of S which is equal to 217 and the value of summation of S into modulus of S minus X bar is equal to 198.53. Therefore mean deviation from mean is equal to summation of S into modulus of S minus X bar that is 198.53 by N that is summation of S which is equal to 217 which is equal to 0.915. From the key idea we know that coefficient of mean deviation is given by mean deviation from mean by mean. Therefore coefficient of mean deviation which is equal to mean deviation from mean divided by mean is given by mean deviation from mean is given by 0.915 by mean that is 7.09. Therefore coefficient of mean deviation is equal to 0.915 upon 7.09 which is equal to 0.129. Hence mean deviation from mean is given by 0.915 and coefficient of mean deviation is equal to 0.129 which is the required answer. This completes our session. Hope you enjoyed this session.