 Hello and welcome to the session. In this session, we shall learn how can we draw inferences from two populations using center and measure or spread from random samples. Whenever two samples are given, we can find its center using mean, median or mode and we can also find its spread using range, interquartile range, etc. Measure of center helps us to know the value around which the most of the values in the data lie. For example, if we want to compare marks of students of two schools, we can collect random sample of marks of students from school A as well as from school B and find the center of the two data. If school A students have average marks, 35 and school B students have average marks of 55, then we can say that school B students higher than school A measure of variation describes the data is spread out. Sometimes the data is clustered around a single value, but sometimes there is a lot of variation in the data. For example, in the series 2, 3, 4, 5, 7, 10, 12, 15. Here the values are clustered in the beginning where they are only 1 unit apart. They start to spread after 5 where they are 2 or 3 units apart. So we can say that with the help of spread, we can draw inferences about two populations like we can know which city has more variation in temperatures. And we can make use of the box and whisker plot, box plot following center and spread of the two data sets can draw inferences about the populations. Let us take an example. The following box and whisker plot shows the amount of calories for the two random samples drawn from fruits and vegetables respectively. What inference can you draw for the calories, food energy of fruits and vegetables? Now we know that this line in box and whisker plot represents lower quartile, the lower line is the median and this line represents upper quartile. As we can see here, most vegetables have calories between 100 and 125 of food energy and most fruits have between 75 and 125 of food energy. And the outliers here show that one fruit has 400 calories and one vegetable has 375 calories of energy. Here we notice that inter quartile range of vegetables will be given by upper quartile minus lower quartile. Here we see that in case of vegetables, the upper quartile is 125 and the lower quartile is given by 15. So we have the inter quartile range as upper quartile that is 125 minus lower quartile that is 50 which is equal to 75. And similarly inter quartile range in case of fruits will be given by upper quartile minus lower quartile that is 165 minus 100. So we have inter quartile range in case of fruits is equal to 165 minus 100 which is equal to 65. And median in case of vegetables is given by 100 and in case of fruits is equal to 125. So median for vegetables is given as 100 and for fruits it is equal to 125. So we can say that although the calories we get from fruits is higher than vegetables but food energy of fruits and vegetables does not vary much. This completes our session. Hope you enjoyed this session.