Population and Sample: Distinction

00:02 Before crunching any numbers and making decisions, we should introduce some key definitions. The first step of every statistical analysis you perform is to determine whether the data you are dealing with is a population or a sample.

00:16 A population is the collection of all items of interest to our study and is usually denoted with an uppercase n.

00:23 The numbers we've obtained when using a population are called parameters.

00:28 A sample is a subset of the population and is denoted with a lowercase n and the numbers we've obtained when working with a sample are called statistics.

00:37 Now you know why the field we are studying is called statistics.

00:41 Let's say we want to perform a survey of the job prospects of the students studying in the New York University.

00:47 What is the population? You can simply walk into New York University and find every student, right? Well, surely that would not be the population of NYU students.

00:58 The population of interest includes not only the students on campus, but also the ones at home on exchange abroad, distant education students, part-time students, even the ones who enrolled but are still at high school.

01:11 Though exhaustive, even this list misses someone.

01:15 Point taken. Populations are hard to define and hard to observe in real life. A sample, however, is much easier to gather.

01:24 It is less time-consuming and less costly.

01:27 Time and resources are the main reasons we prefer drawing samples compared to analyzing an entire population.

01:35 So let's draw a sample then, as we first wanted to do, we can just go to the NYU campus next.

01:42 Let's enter the canteen because we know it will be full of people.

01:46 We can then interview 50 of them.

01:49 Cool. This is a sample drawn from the population of NYU students. Good job.

01:57 Populations are hard to observe and contact.

01:59 That's why statistical tests are designed to work with incomplete data.

02:03 You will almost always be working with sample data and make data driven decisions and inferences based on it.

02:10 All right. Since statistical tests are usually based on sample data, samples are key to accurate statistical insights.

02:17 They have two defining characteristics, randomness and representativeness.

02:22 A sample must be both random and representative for an insight, to be precise.

02:28 A random sample is collected when each member of the sample is chosen from the population strictly by chance.

02:35 A representative sample is a subset of the population that accurately reflects the members of the entire population.

02:43 Let's go back to the sample we just discussed, the 50 students from the NYU canteen. We walked into the university canteen and violated both conditions. People were not chosen by chance.

02:55 They were a group of NYU students who were there for lunch.

02:59 Most members did not even get the chance to be chosen as they were not in the canteen.

03:04 Thus, we conclude the sample was not random.

03:09 But was it representative? Well, it represented a group of people, but definitely not all students in the university, to be exact.

03:17 It represented the people who have lunch at the university canteen.

03:22 Had our survey been about job prospects of NYU students who eat in the university canteen, we would have done well.

03:30 Okay. You must be wondering how to draw a sample that is both random and representative. Well, the safest way would be to get access to the student database and contact individuals in a random manner.

03:43 However, such surveys are almost impossible to conduct without assistance from the university. All right.

03:50 Throughout the course, we will explore both sample and population statistics.

03:55 After completing this course, samples and populations will be a piece of cake for you. Thanks for watching.