 Hello and welcome to the session. I am Deepika here. Let's discuss the question which says the following table shows the ages of the patients admitted in a hospital during a year age in years in the age group 5 to 15 number of patients admitted for sex in the age group 15 to 25 number of patients were 11 in 25 to 35 21 45 to 45 23 45 to 55 14 and 55 to 65 5 Find the mode and the mean of the data given above Compare and interpret the two measures of central tendency Now to find out mean we will use the direct method which is mean x bar is equal to sigma fi xi upon sigma fi where fi is the frequency of the ith class and xi is the midpoint of ith class In a group frequency distribution, it is not possible to determine the mode by looking at the frequencies Here we can only locate a class with the maximum frequency called the model class The mode is a value inside the model class and is given by the formula Mode is equal to f1 minus f0 upon f1 minus f0 minus f2 into h Where it is a lower limit of the model class Size of the class interval Assuming all class sizes to be equal x1 is frequency of the model class is a Frequency of the class in the model class 2 is a frequency of the class succeeding the model class 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 we are given The age in years and the number of patients That is f5. We will write like this Now in the age group 5 to 15 the number of patients admitted was 6 in the age group 15 to 25 the number of patients admitted were 11 and In the age group 25 to 35 Number of patients admitted were 21 and in 35 to 45 Number of patients admitted were 23 and in the age group 45 to 55 Number of patients admitted were 14 and in the age group 55 to 65 Number of patients admitted were 5 Now we will find out the class mark of each class that is we will find out x i which is obtained by Finding the average of its upper and lower limits So for this class it is 5 plus 15 upon 2 which is 10 and For the second class it is 15 plus 25 upon 2 which is 20 similarly for this class it is 30 and for this class 35 plus 45 by 2 which is 40 and for the age group 45 to 55 the class mark is 50 and For the age group 55 to 65 the class mark is 60 Now we require the product of each x i with the corresponding Frequency f i that is we want f i X i so 6 into 10 is 60 11 into 20 is 220 21 into 30 is 6 30 23 into 40 is 9 20 and 14 into 50 is 700 and 5 into 60 is 300 now sigma f i Which is a sum of all? Frequency is equal to 80 sigma f i x i is Equal to 2 a 3 0 so we have mean x bar is equal to sigma f i X i upon sigma f i and this is equal to 2 a 3 0 upon 80 and This is equal to 35.37 Years Now in this table we see the maximum frequency is 23 and The class having the maximum frequency is 35 to 45. So our model class is 35 to 45 low limit of the model class is Which is 35 is the size of the? class interval so H is again F1 is the frequency of the model class which is 23 and F0 is the Frequency of the class preceding the model class which is 21 So F0 is 21 frequency of the class succeeding the model class and this is 14 so F2 is 14 Now we have a formula more is equal to minus F0 upon 2 F1 minus F0 minus F2 into H Now L is equal to 35 Plus F1 is 23 Minus F0 is 21 upon 2 F1 that is 2 into 23 Minus F0, which is 21 minus F2 14 into 10. So this is equal to 35 plus 46 minus 21 minus 14 into 10 and This is again equal to 35 plus 2 upon 11 into 10 and this is equal to 35 plus 20 upon 11 and this is equal to 35 plus 1.8 and this is equal to 36.8 years Hence the mean of the above question is 35.37 years That is on an average the age of a patient admitted to the hospital is 35.37 years and Mode of the above question is 36.8 years That is maximum number of patients admitted in the hospital are of the age 36.8 years approximately Hence the answer for the above question is Mode is equal to 36.8 years Mean is equal to 35.37 years Maximum number of patients admitted in the hospital are age 36.8 Years approximately While on an average The age of a patient admitted to the hospital is 35.37 years So I hope the solution is clear to you Bye and take care