 Hello and welcome to this session. In this session we shall study the concept of samples and populations. Suppose in a city there are various ice cream parlours which sell variety of ice creams like vanilla, butterscotch, almond, chocolate etc. A journalist wants to know which the most famous ice cream parlour is so that he can write an article on it. What will we do? He will ask the people of the city which their favourite ice cream parlour is. But question arise will he ask each and every person in the city to know most famous ice cream parlour? If no, what will we do? The answer is he will select any number of people from the city and ask them about the parlour and will draw a conclusion about the most famous parlour in city. The name of the ice cream parlour which most of the people will take will be the most famous parlours. Suppose there are 300,000 people residing in the city. The journalist chooses any 1000 people to answer the question. Then 300,000 is the population and 1000 is the sample. Thus we can say population is the entire group of people or objects and sample is a part of the population. Remember it is not necessary that population should include people only. Population can be of any item or object, living or non-living. It depends on what do we want to know. For example a factory manufacturer of toys, the owner wants to know how many of them are defective. So he chooses any number of toys and asks how many are defective and draws the conclusion. In this example the toys manufactured is the population and the chosen toys from the sample. Also we know that the sample chosen is random. It means we can select any object or person without any preferences and this is called choosing the sample randomly. Now in the above example we chose 1000 persons from 300,000 people. It means size of the sample depends on the size of the population. It means if we are having 200 objects as population then we can choose sample of 15 objects. We can summarize the above as a sample is some portion of a larger group called the population. Since it is impossible to examine every item in the population a sample is selected to represent the population. After the sample is analyzed the conclusions can be drawn about the entire population. The larger the sample size the more closely it approximates to population. It means our conclusions regarding the entire population will be more accurate. Now we are going to discuss reasonable sample. Now question arises how can we select samples which gives us the most accurate conclusion or prediction. Chosen sample gives us the correct inferences about the population if it satisfies the following conditions and the first condition is sample should be selected as random, second it should be a representative of the population, thirdly it should be large enough to provide accurate data if the sample satisfies these three properties then it is the best sample chosen from the population. Let us take an example, identify the sample and the population and examine whether the sample chosen is reasonable. The school principal wants to organize a total cultural and technical first for the students. He randomly asks 100 students whether they would like to participate in the event or not. Population of the students in that particular school is 2000. Here all the 2000 students form the population and randomly selected 100 students make the sample. So here we have population which is given by 2000 students and the sample that is 100 students. To check whether the sample chosen is reasonable we must see that these three conditions are satisfied by the sample that is sample should be selected at random. It should be a representative of the population and it should be large enough to provide accurate data. Now we know that here the sample is randomly selected so the first condition is satisfied. Now 100 students of school can be of any grade and these students are chosen from the same school so it is a true representative of the population. So second condition is also satisfied and we are choosing 100 students from 2000 students so it is a large enough sample for the school population. Therefore the third condition is also satisfied since all the three conditions are satisfied thus we can say the sample chosen is reasonable. And this completes our session. Hope you enjoyed this session.