Introduction to Population and Sample
In this Post, we continue our discussion on statistics. Before moving towards measures of central tendency and measures of dispersion, it is essential to understand two important concepts: population and sample.
Defining Population
Let us consider a simple example. Imagine an island where the total number of people residing is approximately 100,000. This total number of people is referred to as the population because it represents the entire group of individuals in that specific island.
Collecting Data from the Population
Suppose the task is to collect the weights of all the people in this population. This would require visiting each individual and recording their weight, such as 100 kg or 70 kg. However, logically, it is very difficult to visit and collect data from all 100,000 people. Some individuals may not be available or may be residing elsewhere, making it impossible to gather data from everyone.
Introduction to Sample
In such scenarios, we consider a sample of the population. For example, selecting 10,000 people out of the 100,000 as a sample. This subset is called a sample. Various sampling methods exist, which will be discussed in upcoming lectures. The sample is used to make inferences about the entire population.
Use of Sample in Inferential Statistics
Most inferential statistics use sample data to draw conclusions about the population. For instance, in exit polls during elections, it is impractical to ask every voter whom they voted for. Instead, a sample is taken, and conclusions are drawn about the likely winner based on this sample.
Notations for Population and Sample
It is important to note the notations used in statistics: population size is denoted by capital NN, whereas sample size is denoted by small nn. These notations are commonly used when discussing population mean, sample mean, and other statistical measures.
Summary
This lecture provided a foundational understanding of population and sample, which are critical concepts in statistics. Understanding the difference between these two and their notations prepares us for further study into measures of central tendency and dispersion.
Key Takeaways
- Population refers to the entire group under study, denoted by capital NN.
- A sample is a subset of the population, denoted by small nn, used for analysis when studying the entire population is impractical.
- Sampling allows inference about the population without collecting data from every individual.
- Notations capital NN for population size and small nn for sample size are fundamental in statistics.