 Hello and welcome to the session. In this session, we shall study the concept of how our data collected can be represented such that it describes its center, spread and overall shape. First of all, we shall understand the concepts of center, spread and overall shape. Now, by center of distribution, we mean an observation around which list of the values. The center is a point in a graphic display where about half of the observations are on either side. Now, let us discuss this with the help of an example. And in this example, given distribution of number of miles, Jack rode on a bike for 6 days. And here on this table, in the first column the days are given and in the second column the miles road are given. That is where we are given that on Monday Jack rode 3 miles on Tuesday he rode 6 miles. On Wednesday he rode 4 miles. On Thursday he rode 2 miles. On Friday he rode 4 miles. And on Saturday he rode 8 miles. So, we have the following observations. And the observations are 3, 6, 4, 2, 4 and 8. Which are the number of miles Jack rode on a bike for now arranging the above data from lowest to highest value. We get 2, 3, 4, 4. Now, from this arrangement, we can see that the central value is around 4. Now, for these observations, let us draw a graph. For observations, we have drawn this bar graph. First bar shows that on Monday Jack rode. Then the second bar shows that on Tuesday Jack rode 6 miles. Then the third bar shows on Wednesday Jack rode 4 miles and so on. Also, in this graph diagram, the central height of bar is around 4. So, it is the center of distribution. Another definition of center is that half of the observations should be below the central value and half of the observations should be above the central value or also known as middle value. Now, let us take the spread of the distribution. Now, the spread of the distribution refers to the weight entity of the data. If the observations were of a wide range, then the spread is larger if the observations are clustered around a single value, then the spread is smaller. Now, the history graph is the best graphical display to know the spread of observations. Now, let us discuss an example for this. Now, we are considering the filming distribution of the marks of students. Now here, in this table, in the first column, the marks in the form of intervals are given to us and in the second column, the number of students in the particular intervals are also given to us. Now here, for the marks 0 to 20, the number of students is 5. Then for the interval 20 to 40, the number of students is 0. Then for the interval 40 to 60, the number of students is 20. For the interval 60 to 80, the number of students is 40. And for the interval 80 to 100, the number of students is 10. That is, there are 5 students who scored the marks in the interval 0 to 20. That is, there are 5 students who have scored the marks whenever equal to 0 and less than 20, then you can also see that there are 10 students who have scored the marks greater than equal to 80 and less than 100. And similarly, we can see for the other class intervals also. Now, for these observations, let us draw a histogram. So, for the given observations, we have drawn a histogram. Now, from the histogram, you can see that there are 5 students who have scored marks greater than equal to 0 and less than 20. When most students have scored marks greater than equal to 20 and less than 40, then there are 20 students who have scored marks greater than equal to 40 and less than 60 and so on. Also, in this graphical representation, the observations are concentrated in 60 to 80 marks. Thus, marks are not widely spread. So, as the marks are not widely spread, this means the spread is less. So, we can find out the range of the spread. Now, in this, we can see that range of the spread is from 0 to 40 that is from 0 to 40 number of students. Now, consider this histogram. Now, here you can see that the observations are not concentrated in between any two particular values and the observations are distributed throughout the graph. So, as the observations are distributed throughout the graph, so we see the observations are widely spread. Now, let us see a remark and that is the distribution which is more variable is widely spread. The distribution which is less variable, less spread. Now, let us discuss the shape of the distribution. Now, the shape of the distribution is described by the following characteristics. The first one is symmetry. Now, when it is graphed, a symmetric distribution can be divided at the center so that is the visual image of the other. Now, for example, let us consider histogram in this graph. This histogram is given and here we can see that this graph is symmetric in shape. Now, we have already discussed that a symmetric distribution can be divided at the center so that each half is the visual image of the other. Now, here you can see that the third bar in the given graph is at the center and the bars on either side are mirror images of each other. That is, the last bar is the mirror image of the first bar. The second last bar is the mirror image of the second bar and this distribution is also called normal distribution. Now, let us discuss the next characteristic and that is the number of peaks. Now, the distributions can have few or many peaks. Now, the distribution with one clear peak is called union model and the distribution with clear peaks is called a binary model distribution. Now, for this symmetric distribution, we have one clear peak. So, when a symmetric distribution has a single peak, then it is referred to as a binary shaped distribution. On this histogram, we have a single peak that is the middle part so it is a union model distribution. Now, consider this histogram. Now, this histogram that is the third and the fifth bar a binary model distribution. Now, let us discuss the concept of skewness. When the observations are displayed graphically, then some distributions have more observations on one side of the graph than the other. Now, the distributions with most of the observations on the left towards lower values are said to be skewed right distributions with most of the observations on the right towards higher values are said to be skewed left. Now, in this histogram, most of the values are concentrated towards higher values so it is skewed to the left. Now, let us discuss uniform or flat distribution. Now, consider this given histogram. Now, here we can see that the observations in a set of data are equally spread across the range of distribution. So, this distribution is called a uniform distribution. So, here the observations in a set of data are equally spread across the range of distribution. So, this distribution is called a uniform distribution and a uniform distribution has no clear fields. So, in this session you have learnt about the concept of how a data collected can be represented such that it describes its center, spread and overall shape. So, this completes our session. Hope you all have enjoyed the session.