 In this video, we will try and find out mean of group data. Now what changes when we have group data is that instead of the numbers or the data in individual form like this, like 2014, 13, 20, whatever, we have group data. For example, if we are talking about say distances that people walk in the morning, for example. So let's start with 0 to 5 kilometers. So everything is in kilometers and I'll just put different colors here. Next group would be 6 to 10 kilometers. There are so many people walking and we just want to make considerable groups so that we can classify people to be novices to proper athletes. So let's say we take such distances here and the last one is 16 to 20 kilometers. I'll have a vertical line over here. I'll separate these groups by horizontal lines like this and now I'll just say these are number of people walking these distances in the morning. Let's say there are six people walking 0 to 5 kilometers in the morning. Then there are only two people who walk 6 to 10 kilometers. Then there are three people who walk 11 to 15 kilometers and there are say four people who walk 60 to 20 kilometers. What if we wanted to calculate the mean distance these many people walk? So what is the process for calculating the mean? Let's see. First step is to find out the mean of these groups and we also call it class mark. So these things are known as classes. So class of 0 to 5 or class of 6 to 10, something like that. And we want to calculate class mark for each. Let's write it here. So class mark, all right, and class mark is basically the mean of these two values. So if you wanted to calculate class mark for 0 to 5, I'll just show for the first one will add these two divided by 2 because there are only two quantities that we're looking at and it will be 2.5. Similarly, the class mark for 6 to 10 is going to be 6 plus 10 divided by 2 and it gives us 8. So we don't know how many kilometers these six people walk or like one of them could just be walking 1 kilometers. Two of them could be walking 3 kilometers, but we're just assuming that all these six people walk 2.5 kilometers. That's the meaning of class mark here. Similarly, these two people are supposed to be walking 8 kilometers. Let's calculate the class mark for 11 to 15 and that's going to be 13 kilometers. And for 16 to 20, the class mark will be 16 plus 20 divided by 2, which is going to be 18 kilometers. Let's represent this as Xi. Usually we keep a bar over it to suggest that it's a mean of the class or a class mark. So this is Xi. Number of people is nothing but the frequency and it's Fi. And now to calculate the mean distance, we need to find the total distance that all these people walked divided by total number of people, right? The total distance can be calculated by multiplying the number of people walking that particular mean distance in each group. So that is summation of Fi and Xi bar divided by summation of Fi. And summation of Fi is nothing but total number of people. Let's try and calculate this. So if we talk about summation Fi Xi, it will be say 6 people walking 2.5 kilometers plus 2 people walking 8 kilometers. Let's write it like that. So 2 people walking 8 kilometers plus 3 people walking 13 kilometers plus 4 people walking 18 kilometers. And we will divide this by summation of Fi or total number of people and that's 6 plus 2 plus 3 plus 4, which is 15. So if we compute the numerator here, we get 142 divided by 15. And so we get the mean as 9.46 kilometers. The meaning of this mean is that the mean distance walked by all these people is 9.46 kilometers. Note that only the way of representation of data is changed. We instead of having exact distances walked by these many people, what we have is the range of distances given for some people. And whenever data is given in such a form, which is basically the grouped data, we want to find out the class mark first, which is basically the mean of those classes. So these are basically classes. We have to calculate the class mark and then we treat it as a mean and then we put the summation Fi in the numerator. And in the denominator, we have summation of Fi or the total of frequencies. And that gives us the mean of grouped data.