 Hello and welcome to the session. I am Vipika here. Let's discuss the question which says The length of 40 leaves of a plant are measured correct to nearest millimeter and the data obtained is represented in the following table now if the length in millimeter is 118 to 126 then the number of leaves and if the length is 127 to 135 then the number of leaves is 5 Length is 136 to 144 then the number of leaves is 9 For 145 to 153 it is 12 for 154 to 162 It is 5 for 163 to 171 it is 4 and for 172 to 180 it is 2 Find the medium length of the leaves find the cumulative frequencies of all the classes That is number of observations divided by 2 frequency is greater than and nearest to and upon 2 That will be our medium class. Here is the formula medium is equal to the frequency of class which is the class size So this is a key idea behind our question We will take the help of this key idea to solve the above question. So, let's start the solution Now in this question the data is not continuous The data needs to be converted to continuous classes for finding the medium Since the formula assumes continuous classes out to make it continuous We will subtract 0.5 of each class and We will so the classes then change to 117.5 126.5 126.5 to 135.5 and 135.5 144.5 144.5 153.5 153.5 162.5 162.5 171.5 and 171.5 to 180.5 That is the frequency of each class is given now we will find the cumulative frequencies of Let us make a column for cumulative frequency So for this class it is 3 now for the class 126.5 to 135.5. It is 3 plus 5 8 Again for this class it is 8 plus 9 17 Now for this class it is 17 plus 12 29 And 29 plus 5 34 34 plus 4 38 and 38 plus 240 So n is 40 Therefore n by 2 is equal to stable we see that 140 raised to n by 2 that is 20 classes 4.5 to 153.5 So we have n is equal to which is a low limit of the median class 144.5 the cumulative frequency class which is 12 equal to 12 is equal to according to a key idea The reducer formula median is equal to n by 2 minus cf upon f into h substituting these values is equal to 4.5 which is 20 minus cf 17 upon f which is 12 is equal to 144.5 plus is equal to 144.5 plus 9 upon 4 and this is again equal to 144.5 therefore median is equal to 146.75 the median length 146.75 Millimeter is the answer for the above question is median length is equal to 146.75 millimeter I hope the solution is clear to you. I will take care