< Statistics and Probability Definitions

In statistics, a population is defined as a whole group of people or objects from which samples can be taken. A population is the opposite of a sample, which is a fraction or percentage of a group. For example, if you were interested in surveying dog owners to find out their preferred brand of dog food, the population would be all dog owners in the United States. It would be impractical to survey every single dog owner in the country, so you would instead take a sample of dog owners. Note that if you did manage to survey everyone in the population, it would actually be called a census. The U.S. Census is one example of a census.

In most cases, it’s impractical to survey everyone in a population due to time constraints or other factors. Imagine how long it would take you to call every dog owner in the U.S. to find out what their preferred brand of dog food was! In addition, sometimes people either don’t want to respond or forget to respond, leading to incomplete censuses. Incomplete censuses become samples by definition.

Now that we’ve defined what a population is, let’s discuss why populations are important in statistics.

## Why Populations are Important

Populations are important because they allow statisticians to make inferences about a larger group based on information gathered from a smaller group (i.e., the sample). This process of making inferences about a population based on information from a sample is called statistical inference. Statistical inference allows us to make predictions about populations based on data from samples. For example, if we surveyed 100 dog owners and found that 60% of them preferred Brand A dog food, we could then infer that 60% of all dog owners in the United States prefer Brand A dog food.

There are two types of statistical inferences: point estimates and confidence intervals. Point estimates are single values that are used to estimate population parameters (such as means, proportions, and variances). For example, if we wanted to estimate the mean age of all dog owners in the United States, we could use the point estimate provided by our sample mean age. Confidence intervals are used when we want to estimate an interval or range within which the true parameter value falls with some degree of confidence (usually 95%). So using our previous example, we could say with 95% confidence that the true mean age of all dog owners in the United States falls between X and Y years old.

## Population in Statistics: Conclusion

In statistics, populations are defined as groups of people or objects from which samples can be taken. Populations are important because they allow statisticians to make inferences about groups based on information gathered from smaller samples taken from those groups—a process called statistical inference. Without populations, it would be impossible for us to make predictions about groups of people or objects based on data collected from smaller samples!