 Let us learn how to compute the median of grouped data and for that we will need the group data and The group data Will be like this and let's say this data is about the percentage that different students have got in the class so this class means the percentage range and Frequency is number of students busy. So this is how this table can be read But the heading is class because we are talking about range of percentage that different students have received So just to ease out so this table is telling us about the percentage marks different students have got and our objective here Is to find the median of this particular group data? What is median again? Median is an observation. So it's percentage marks here Just writing it down so that it's easier to understand in the context of this example So median is going to be the percentage marks in all these observations Below which and above which are equal number of observations So how do we find that particular midpoint of marks out of all the observations? The first challenge is of course, we do not even know what are different percentages received by the students These two students who have got percentage range from 10 to 20 percent They might have got 11 and 12 percent or 13 or 15 percent and we don't know about that We just know that there are two students who have received 10 to 20 percent four students who received 20 to 30 percent and so on So how do we start? First of all, let's look at this third column that we have in the third column We have written cumulative frequency. So this F stands for frequency. Now. What is cumulative frequency? Cumulative frequency adds up the existing frequency of that class and all the previous frequency So for 10 to 20 percent, there are two students, but there are no previous classes So cumulative frequency is two here for 20 to 30 percent What this is saying is that how many students got 20 to 30 percent as well as 10 to 20 percent So total six students four plus two adding these two So six students have got percentages less than 30 Similarly, the cumulative frequency for the third class, which is 30 to 40 percent is two plus four plus three, which is nine And then similarly cumulative frequency for 40 to 50 percent is going to be nine plus six, which is 15 And for the last class the cumulative frequency Tells you all the number of students and this is 20 This is also n or the total students or total frequency I'll just write total frequency or you could say a total number of observations and this is an important parameter for us Now we know that median is an observation which is at the middle of all the observations So there are n by two observations below it n by two observations above it So first this observation is going to be somewhere above n by two observations for sure and so We can find something called as median class So we first have to take out a median class where we are sure that our median observation lies and that's why We have to find what is n by two in this case n by two is 20 over 2 and that is going to be 10 and so Because n by two is 10. I'll just quickly write it here as well n by two is 10 So we want to isolate the class or highlight a class Where the number of observations or the cumulative frequency reaches above 10, right? So we have to find a cumulative frequency in the table which becomes greater than n by two for the first class 10 to 20 cumulative frequency is 2 then it's 6 then it's 9 and when this CF or the cumulative frequency Is 15 it it becomes greater than n by 2 for the first time and that happens for this 40 to 50 class and Therefore the median class is 40 to 50. We also know that there are six observations in this class So the frequency for this is 6 now There is another term called CF naught CF naught is the cumulative frequency of the class before the median class class before median class is 30 to 40 and The CF naught or the cumulative frequency until that class is 9 in this case We are going to use this in our computation now the formula for median is given as follows We write the lower limit of the median class first which is given by L and We act to it the fraction where the numerator is n by 2 minus CF naught or divided by The frequency of the median class and this fraction is multiplied by H Which is the range of the class now we put all the values So L is 40 in this case because 40 is the lower range of the median class Plus n by 2 is 10. So 10 minus CF naught is 9 divided by the frequency of the median class, which is 6 Times the range of the class and that is 10 and this gives us the median as 40 Plus 10 over 6, which is 41 point six six and this is how we can find the median of a group data