 Last class, we talked about bar chart and pie chart. We will talk about stack bar chart and histogram in this video. Stack bar chart is a variation of standard bar chart. We saw that in a last video that we can use bar chart for comparing the individual data. In the last class, we saw the similar chart where comparing grade 9, 10, 11, 12 students, boys and girls, their absentee rate for boys is more compared to girls. And also we saw that in a grade 9, it is less compared to grade 12. Same chart can be represented as the stack bar chart that is the both values will be stacked. The only drawback here is it is not clearly showing how much differences from boys and girls. For example, here you can see that there is a difference boys absentee rate is on average high on all the grades compared to girls. But in this chart it is not clear, but this is also another way of representing bar charts called stack bar chart. So, there is a variation of stack bar chart that is what we saw in last slide. This is the stack bar chart, the variation is converting it to a 100 percentage. So, here the value will be represented for the percentage instead of the absolute value, say 22 percent of boys absentee average rate for grade 9, here that will be represented as a percentage compared to total value. So, we know that that is a stack bar chart adjusted for the percentage. So, this is a simple stack bar chart. Let us move on to the other type of chart called histogram. In histogram, we want to show the distribution of numerical values, the input values split into several bins and plotted. The distribution of numerical values, what we mean by distribution of numerical values is for example, you have a class of 60 students, you have a table of class of 60 students, student ID from 1, 2 to 60 students and you have the marks in subject A. Consider that you have a marks in subject A and say 90, 75, 42, something like that. So, you have these marks of class of 60 students in a subject A, you want to represent this in a bar chart. What happens in bar chart? It can represent only the average value or all the students marks can be shown in the bar chart, but it will be too clumsy because there are 60 students. Instead, you can show the distribution of marks in the among this class students, histogram can be used. What we have to do? We have to split these scores into several bins. For example, consider the mark is for 100. If the exam is for 100 marks, you can make several bin of say I want to know how many students got 0 to 10 marks, how many students got 10 to 20, how many students got, so something like that. So, you will have a 92 100. So, basically what you have to do, you have to calculate how many students got mark from 0 to 10, say 7 students, say the 8 students, again there are 10 students, here 10 students. So, some numbers like that. So, it will show, if you show this data in a plot, it will show that how your marks are distributed in your class. The students performance in the class on a subject A is distributed in several range. So, marks of the students in course A can be shown as an histogram. So, let us see these bins. This is the histogram. Here, let me delete this bin value. So, if you look at this, there are like 3 students who got marks from 38 to 38. So, there are no students below 28 and there are no students above 98. So, there are only 2 students who got above 88. And there are 5 students who got 38 to 48. So, most of the students that is 28, 38, 41 students in your class or around from 48 to 78 or from 50 to 80. Or you can see the majority of students that take most 30 students of your class is from 50 to 70. So, these kind of distribution will tell you that how students performance in your class is distributed across this score. So, histogram can be used to identify the distribution of marks in the class or comparing this distribution among 2 courses, something like that. So, you can make histogram by simple using Excel or Google Sheets. You can use some scripts to create histogram. So, we saw histogram now. List down the common mistakes people do in using histograms. Please pass this video, list down the common mistakes after listing it down, resume the video to continue. So, in last slide we saw 7 bins. Why there are 7 bins? We will ask like why there are 7 bins and why the marks are distributed across 28 to 38 and 88 to 98. Why cannot we have only 5 bins? Why we cannot have only 3 bins? Say less than 40, 40 to 80, 80 to 100. Why we have 7 bins? So, if you have several bin sizes say instead of 7 if I want to use 10 bins or if you have 10 I want to use 5 or 3 bins, the conclusion might have a difference. Suppose you might say that lot of students scored less than 40, lot of students who are in the range of 50 to 70 now might have moved to less than 60 and more than 70 to 80 something like that. So, conclusion inference might vary based on the bin size also. So, you have to be careful in using these bin sizes and why you pick these kinds of bins should be supported and argued correctly. And histogram can compare 2 groups for example, marks in the math thesis science that is good. And the important point is all the bin size should be equal. You should not have a bin for example, I was telling you cannot have a bin one bin of less than 40 marks, 40 to 80 and 80 to 100. The bin size is not equal you know since this is 40, 40 this is 20. So, this is not correct. Make sure you have all the bins should be equal also when you compare marks A to marks B, make sure the comparing the bin size is same. Also why we are picking several bin sizes, try several bins and compute the histogram and see which one makes sense and you should have stronger argument why you pick that bin number equal to 7 or 8. In excel you can change the bin size or number of bins to be used in the histogram easily. I pick the bin size of 28 to 38 instead you can say no I want a bin from 20 to 30, 30 to 40 that is all possible. So, make sure you have a bin size and number of bins selected properly when you use the histogram. So, in this video we saw stat bar chart and the histogram and we will see some more charts in the next video. Thank you.