 Let us learn how we can compute mode of group data. So let's first create groups so we will have some groups which is known as class as well and Each of these groups will have some observations in them, which is known as frequency of those groups So let's say we have classes from 5 to 10 then 10 to 15 15 to 20 20 to 25 25 to 30 etc. Now each of these classes will have some frequency list So let's say 5 to 10 class has six observations 10 to 15 as 3 then 15 to 20 has five observations 20 to 25 has seven observations and 25 to 30 has one observation. Let me just arrange them properly. So this has five then seven and One so now first step in order to find the mode of the group data is to find modal class and the modal class is class with highest frequency and we can see here that the class with highest frequency is with the frequency 7 because that's the highest frequency and 20 to 25 is the class where there are most observations and therefore this is modal class. The frequency associated with the modal class is known as F1 or we will call it F1 This is just a convention. The frequency of the class earlier to the modal class We can write F0 for it. We need that in the mode formula and the frequency associated with the class after modal class is F2 We know and we need F0 and F2 in the formula for mode So now let's see what is the formula for mode. This is how I like to Remember the mode formula. So it starts with L. L is basically the lower limit of the modal class which is 20 here Then L plus there is some ratio and ratio times H and H is the class length Let me just quickly write H is the class length which is five here because every class is of five data points So what is this ratio that I'm writing here? So there is numerator and denominator It is in the form of X divided by X plus Y Now what is this X? X is the subtraction of F1 and F0. So basically F1 minus F0 is X and F1 minus F2 is Y and this is how this formula is written If we want to simplify this we can write it as L plus F1 minus F0 in the numerator I think I need more space in the denominator. So F1 minus F0 plus F1 minus F2 times H Which is nothing but L plus inside the bracket again F1 minus F0 divided by so F1 plus F1 which is 2 F1 minus F0 minus F2 Times H. So now let's compute mode for this particular example The L in this case is 20 plus the value of X here Which is F1 minus F0 is 7 minus 5 which is 2 divided by 2 again Big for For X in the denominator plus Y. Y is F1 minus F2 which is 7 minus 1 which is 6 Times the length of the class which is 5 And if we compute this we get 20 plus the ratio becomes 2 by 8 Which is nothing but 1 by 4 times 5 which is nothing but 20 plus 5 by 4 Which is 20 plus 1.25 or 21.25 and 21.25 is the mode for this example