 Hello, and welcome to the session. I am Deepika here. Let's discuss the question which says The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality Find the medium, mean and mode of the data and compare them Monthly consumption in units and number of consumers for 65 to 85 Number of consumers are four for 85 to 105 number of consumers are five For 105 to 125 it is 13 for 125 to 145 It is 20 for 145 to 165 it is 14 165 to 185 this eight and 185 to 205 it is four Now we know that x1 is equal to sigma fi Xi upon sigma fi where fi is the frequency of the i-th class Xi is the classmark of the i-th class that classmark is equal to upper class limit plus lower class limit upon two Now we know that the median is a measure of central tendency Which gives the value of the middle most observation in the data? Now in a group data We may not be able to find the middle observation by looking at the cumulative frequencies as The middle observation will be some value in a class interval It is therefore necessary to find the value inside the class that divides the whole distribution into two halves But this class find the cumulative frequencies of all the classes in the class whose cumulative frequency is greater than called the median class median class we use the formula Udm is equal to is number of observations f is equal to cumulative frequency the class Is reading the median class is the frequency of the median class H is the class size How to find more we will first find the model class the class having maximum frequency Then we will use the formula mode is equal to class f1 minus f0 upon 2 f1 minus f0 minus f2 into h where it is a Lower limit of the model class h is the size of the class interval f1 is the frequency of the model class f0 is the frequency in the model class is the Frequency of the class Succeeding to model class. This is a key idea behind the question We will take the help of this key idea to solve the above question. So let's start the solution Now we are given monthly consumption in units Consumers weekly consumption is from 65 units to 85 units Then the number of consumers are four for 85 to 105 It is five For 105 to 125 it is 13 and for 125 to 145 It is 20 now for 145 to 165 it is 14 and 165 to 185 It is 8 for 185 It is 4 Now that is we will find the class mark of each class We find the class mark of each class average of it Upper 5 is 65 plus 85 upon 2 which is 75 5 to 105 is 85 plus 105 upon 2 that is The class 125 to 145 it is 135 and the class mark is 155 is 175 of the class 185 to 205 is 195 that is 155 to 170 into 175 is 1400 Frequencies that is sigma 5 is equal to 68 Similarly, we will find sigma f5 xi is equal to 9 3 2 0 Therefore, we next bar is equal to Sigma f5 xi upon sigma f5 is equal to 168 is equal to 137 point 05 unit is equal to 137 point 05 units Let us find the mode of the given data Now from this table we observe the maximum frequency Even the maximum frequency is 125 to 145 125 to 145 125 that is the load limit of the model class H the size of the class interval is 20 The frequency of the model class is also 20 to 13 That is the frequency of the class preceding the model class the frequency of the class succeeding the model class so that 0 is 13 Substitute these values in the formula mode is equal to 1 minus f0 upon 2f1 minus f0 and this is equal to 125 F1 is 20 minus 13 upon 2f1 2 into 20 minus 13 minus 14 into and this is equal to 125 plus 7 minus 27 this is 13 into 20 and this is again equal to 125 plus 140 upon 13 and this is equal to 125 plus Now 130 upon 13 is equal to 10 upon 7 6 therefore load is equal to 5 7 6 units The medium of the given data to find the medium the cumulative frequencies of all the classes n and y to column for cumulative frequency frequency of this class is 4 and cumulative frequency of this class is 4 plus is equal to 9 the frequency of this class is 9 plus 13 is equal to 22 the cumulative frequency of this class is 22 plus 20 which is equal to 42 the frequency of this class is 42 plus 14 is equal to 56 plus 8 is equal to 64 and cumulative frequency of this class is 64 plus 4 and this is equal to 68 now in this distribution n is 68 so n by 2 is equal to 8 upon 2 which is equal to 34 now we will locate cumulative frequency is greater than frequency 42 is greater than 125 up to 145 is the medium class in class we use our formula medium is equal to is the lower limit of the medium class is 125 division is 68 and CF the medium class is frequency of the medium class is 20 and this is 20 to take these values in the formula medium is equal to all plus under 2 minus CF upon f into h we get medium is equal to 125 268 upon 2 minus 22 upon 20 is equal to 125 plus minus 44 upon 2 into 20 into 20 and this is again equal to 125 plus upon 40 into 20 so we have is equal to 125 plus 12 which is equal to 137 units the medium and mode of the given distribution medium is equal to 137 units and medium is equal to 137.05 units and mode is equal to 135.76 units the 3 measures are approximately the same so from above results we conclude that the 3 measures correctly for the above question is is equal to 137 units is equal to 137.05 units is equal to 135.76 units the 3 measures approximately the same in this case but the solution is clear to you bye and take care