 Hello and welcome to the session. In this session we are going to discuss which appropriate statistics should be used to measure, center and spread for two or more data sets according to the shape of the data. Now here we shall discuss three shapes of the distribution that is symmetric, skewed to the right and skewed to the left. We can display a data set in the form of a histogram or box plot or stem plot or we can also display a data set in the form of a dot plot and the shape of these displays can be symmetric skewed to the right or skewed to the left. Now we shall see the three shapes with the help of a curve. If the curve is bell shaped with the peak and central value like this then we say that it is symmetric. See this graph here the peak is at the center and it is at the point of mean or median. Here we should note that at this point mean is equal to median so we say that the curve is symmetric also here mean is equal to median and here we have seen that in this bell shaped curve the peak is at the center and it is the point of mean or the median and here we should note that mean is equal to the median. Now if the data values are more clustered to the left side then the curve will be like this. Here the tail of the curve is to the right towards the higher values then we say that the curve is skewed to the right. Here we should note that mean is greater than the median. From this graph it is clear that mean is greater than the median. Now if the data values are more clustered to the right side then the curve will be like this. Here the tail of the curve is to the left towards the smaller values and therefore we say that the curve is skewed to the left and here mean is less than the median. From the graph it is clear that mean is less than the median. We should also note that longer the tail more spread is the data. Now we are going to discuss appropriate measures of center and spread of data. In skewed distributions median is an appropriate measure of center. When the distribution is symmetric and has large values then mean is an appropriate measure of center. Now when the data display is in the form of box plot then median is an appropriate measure of center and interquartile range is an appropriate measure of spread and when we use mean as a measure of center then measure of spread is calculated by using standard deviation. Now we know that the spread of the data refers to the variability of the data. If the data cluster around a single central value then spread is small. If we see this histogram we find that here values are clustered at 5 that is values are clustered at 0.5 so we say that the spread is less. Here we also notice that the values are clustered around the central point 5 so we have less spread. Now if we see this histogram here the values move further from the central value so it is more spread. Thus we say that the further the values from the center the greater the spread or variability of the data. Now we are going to discuss standard deviation. The standard deviation is the measure of how spread out the data is. It indicates the average distance from the mean for the set of values also greater standard deviation shows more distance from the mean for the set of values. Now we are going to discuss how to compare standard deviation with the help of graphs. If we consider this graph we see that here the red curve shows one data set and this blue curve shows another data set. Now in this graph that is graph one we see that there is symmetric distribution for both the curves and both the curves have same mean. We can see that the peaks of both the curves lie on the same line. So we can say that the center of the two data sets is same but the red curve is widely spread than this blue curve. So red curve shows greater standard deviation than blue curve. So we can say that red distribution has greater spread than blue distribution. So in this session we have learned which appropriate statistics should be used to measure center and spread for two or more data sets according to the shape of the data. This completes our session. Hope you enjoyed this session.