ISIA P&S L1 C2 S1
Intro Stats: Islamic Approach -- Part 2: Probability and Statistics -
Lecture 1: Random Samples, Concept 2: Populations Slide 1: Basic Definitions & Examples
In statistics, the target of our study is a population. The name suggests people in a city, country, or some other collection. This is indeed a correct and important possibility. However, statisticians use the term in a more general sense. ANY collection of objects can be called a population. Generally, statistical methods are useful only when the population is so large that direct study of the entire population is not possible. In this case, a small random sample is taken from the population, and this small sample is studied to find out answers to questions about the the full population. The main goal of probability and statistical theory is to learn how we can make inferences about the population from a random sample. The CONCEPT under study in this set of slides is the POPULATION -- this concept will be illustrated and clarifed by several examples.
C2 S1: Populations: Basic Definitions and Examples
The table above shows a population of 4 people, and provides some characteristics of each. In general, a population is like this: a collection of objects, each of which have different characteristics.
In general populations are VERY LARGE --- for example the population of Pakistan. This is what creates the need for statistics. We cannot directly analyse the full population. Indeed, the data for the full population is not available. But we NEED to know what is happening to the incomes of the population as a result of policies adopted by the government. Income is just one example. We might need to know about health, family size, housing, nutrition, etc. for the whole population. It would be EXTREMELY expensive to go and collect information for ALL the people in the population.
For many burning issues of economic policy, we NEED to know what is happening to the population, for example, whether poverty is increasing or decreasing. It is too expensive to find out by getting information about everyone. SO HOW CAN WE FIND OUT? The solution is to take a RANDOM SAMPLE. Under conditions that we will discuss and study, the random sample will look like the original population. By doing calculations for the random sample, we can make INFERENCE about the population. How this is done is the subject of Probability and Statistics. Probability teaches us about how the random sample is related to the population. So if we know the population, we can use probability to find out what random samples from the population should look like. Statistics works in the opposite direction. Given a random sample, we try to find out what population must look like.