 I'd like to discuss a very relevant thing with you. So there is all often debate whether Virat Kohli's waiter or Sachin Tendulkar is better. The image of Sachin Tendulkar's has been taken from Creative Commons license 3.0 and Virat Kohli's image is from Pixar Bay. Usually people say that Virat has scored 13,848 runs, but Sachin has scored 18,426 runs. But then people often argue that average or the batting average or the mean of all the scores by Virat, which also means that the number of runs he scores per innings is 58.7, whereas for Sachin it is 44.8. But Virat hasn't finished his career yet. So it's always debatable who is going to be better. So whenever you come into such arguments, always remember that there are different parameters that you look at when you want to compare between the datasets or performances. Important to note that arithmetic mean is just a fancy term for the word average. We usually come across the word average, but we are looking at arithmetic mean and these words are used interchangeably. There are different kinds of mean that we need to study and in this particular video we'll be looking at arithmetic mean. But why do we study arithmetic mean? What is the point of understanding arithmetic mean and how is it useful in real life? So why do we study arithmetic mean? So let's say there is a student called Manohar and Manohar is concerned about his marks say in English and then in math I'll use different color for math and let's use say this color for history. So I'll be just taking three subjects and Manohar term one. So this one signifies Manohar's performance in these three subjects in term one and then Manohar's performance in the second term. Let's just create a nice quick table to write down marks that he got in term one and term two. So in English let's say he scored 65 out of 100 in term one. In math Manohar scored say 72 out of 100 and in history he was in that grade. So he scored say 57. So let's see after term one how his performance improved or was there any improvement at all. So let's say Manohar scored 73 in English. In math he scored say 75 and in history his performance actually dipped. So he could just score 40 and now the question is did Manohar really improve his performance? It's quite clear that in term two in English his marks were better. In maths also his marks were better but in history his performance was a little down. There is a parameter which is called arithmetic mean and in such scenarios what we could do is we can find arithmetic mean of all the marks that he got and look at the performance overall. So this is a measure of overall performance you could say and what we do is that we total all the marks and we divide the number of papers or number of exams that he gave. So let's say this is mean and let's go for another color. So let's write the mean for Manohar in term one and term two. I just quickly revise how we can find out mean. So arithmetic mean is basically found by a total score and in the denominator how many attempts were there to get that score or in this case attempts is basically the papers so total papers or total attempts I will just write it as general so total attempts. So to find the mean score of Manohar in term one we will add all the scores and divided by three because there were three papers. So for term one the mean term one mean is 65 plus 72 plus 57 divided by three and this comes out to be 194 divided by three which is 64.67. So let's just write this mean here 64.67. Manohar scored 64.67 marks on an average in each paper. This also means if Manohar appears for any other exam like say Hindi or French whatever his expected score is going to be 64.67. So out of 100 he is scoring 64.67. Now let's see what is the performance of Manohar in term two. Let's just add all the numbers that we have for term two. So for term two the mean for Manohar's marks is 73 plus 75 plus 40 divided by three. Again this three refers to three papers that he appeared for and this comes out to be 188 divided by three. It appeared as if Manohar was improving because he improved in English, he improved in math as well. So for two subjects he did improve but overall his performance actually dipped and this comes out to be 62.67. Let's write this mean here. So in fact his performance dipped in the term two that's what the marks suggest here. After finding out mean we get the idea whether there is a performance dip or performance improvement in this case and mean actually is a measure of calculating the performance when there is a varied data set that is available to us.